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Preprints

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville VIC 3010 Australia
aram@unimelb.edu.au

(36) The Steinberg-Lusztig tensor product theorem, Casselman-Shalika and LLT polynomials, (with M. Lanini), preprint 2018, arXiv1804.03710.

(35) A Fock space model for decomposition numbers for quantum groups at roots of unity, (with M. Lanini and Paul Sobaje), preprint 2016, arXiv1612.03120.

(34) Two boundary Hecke algebras and combinatorics of type C, (with Z. Daugherty), preprint 2015, arXiv????.????.

  • Daugherty-Ram Abstract
  • Daugherty-Ram Contents
  • Daugherty-Ram Section 1. Introduction
  • Daugherty-Ram Section 2. The two boundary Hecke algebra
  • Daugherty-Ram Section 3. Calibrated representations of Hkext
  • Daugherty-Ram Section 4. Classification of irreducible representations of H2
  • Daugherty-Ram Section 5. Representations of Bkext in tensor space
  • Daugherty-Ram References

(33) Cyclic representations of the periodic Temperley Lieb algebra, complex Virasoro representations and stochastic processes, (with F.C. Alcaraz and V. Rittenberg), preprint 2014, arXiv1402.5990, appeared in in J. Phys. A: Math Theor. 47 (2014) 212003.

(32) Generalized Schubert Calculus, (with N. Ganter), preprint 2012, arXiv1212.5742, appeared in J. Ramanujan Math. Soc. 28A (Special Issue-2013), 149-190.

  • Ganter-Ram Section 1: Abstract, Introduction and Acknowledgments
  • Ganter-Ram Section 2: The Schubert calculus framework
  • Ganter-Ram Section 3: The moment graph model
  • Ganter-Ram Section 4: Partial flag varieties and Bott-Samelson classes
  • Ganter-Ram Section 5: Schubert classes
  • Ganter-Ram Section 6: Products with Schubert classes
  • Ganter-Ram Section 7: Schubert classes and products in rank 2
  • Ganter-Ram Section 8: The calculus of BGG operators

(31) Hopf algebras and Markov chains: Two examples and a theory, (with P. Diaconis and A. Pang), preprint 2012, arXiv1206.3620, appeared in Journal of Algebraic Combinatorics 39 (2014) 527-585 http://dx.doi.org/10.1007/s10801-013-0456-7.

(30) Affine and degenerate affine BMW algebras: Actions on tensor space (with Z. Daugherty and R. Virk), preprint 2012, arXiv1205.1852, appeared in Selecta Mathematica 19 no. 2 (2013) 611-653.

  • Section -2: Contents
  • Section -1: Abstract
  • Section 0: Introduction
  • Section 1: Actions of general type tantalizers
  • Section 2: Actions of classical type tantalizers
  • Section 3: Central element transfer via Schur-Weyl duality
  • Section 4: Symplectic and orthogonal higher Casimir elements

(29) Symmetry breaking, subgroup embeddings and the Weyl group (with D. George, J. Thompson and R. Volkas), preprint 2012, arXiv1203.1048, appeared in Physical Review D 87 105009 (2013) [14 pages] http://prd.aps.org/abstract/PRD/v87/i10/e105009.

(28) Affine and degenerate affine BMW algebras: The center (with Z. Daugherty and R. Virk), preprint 2011, arXiv1105.4207, appeared in Osaka J. Math 51 (2014), 257-283.

  • Section -1: Contents
  • Section 0: Abstract
  • Section 1: Introduction
  • Section 2: Affine and degenerate affine BMW algebras
  • Section 3: Identities in affine and degnerate affine BMW algebras
  • Section 4: Central element transfer via Schur-Weyl duality

(27) Universal Specht modules for cyclotomic Hecke algebras (with A. Kleshchev and A. Mathas), preprint 2011, arXiv1102.3519, appeared in Proc. London Math. Soc. (3) 105 (2012) 1245-1289.

(26) A probabilistic interpretation of the Macdonald polynomials (with P. Diaconis), preprint 2010, arXiv1007.4779, appeared in The Annals of Probability 40 (2012) Vol. 40 No. 5, 1861-1896, DOI 10.1214/11-AOP674, arXiv1007.4779, MR??????

(25) Universal Verma modules and the Misra-Miwa Fock space (with P. Tingley), preprint 2010, arXiv1002.0558, appeared in Int. J. Math. and Math. Sci., special issue on “Categorification in Representation Theory”, Volume 2010, Article ID 326247, 19 pages, doi:10.1155/2010/326247.

(24) Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words (with A. Kleshchev), preprint 2009, arXiv0909.1984, appeared in Math. Ann. 349 (2011), 943-975, DOI 10.1007/s00208-010-0543-1.

(23) Homogeneous representations of Khovanov-Lauda algebras (with A. Kleshchev), preprint 2008, arXiv0809.0557, appeared in J. Eur. Math. Soc. 12 (2010), 1293-1306, DOI 10.4171/JEMS/230.

(22) Alcove walks, buildings, symmetric functions and representations (with J. Parkinson), preprint 2008, arXiv0807.3602.

(21) MathML for mathematics research articles (flexible version), stable version, pdf version, preprint 2008.

(20) A combinatorial formula for Macdonald polynomials, (with M. Yip) preprint 2008, arXiv0803.1146, Adv. Math. 226 (2011), 309-331, doi:10.1016/j.aim.2010.06.022.

  • Ram-Yip Section 1: Abstract, Introduction and acknowledgements
  • Ram-Yip Section 2.1: Double affine Weyl groups
  • Ram-Yip Section 2.2: Double affine braid groups
  • Ram-Yip section 2.3: Double affine Hecke algebras
  • Ram-Yip section 3: Macdonald polynomials
  • Ram-Yip section 4.1: Examples of Macdonald polynomials type A1
  • Ram-Yip section 4.2: Examples of Macdonald polynomials type A2
  • Ram-Yip Appendix A: Bijection between W and alcoves in type SL3

(19) Combinatorics in affine flag varieties, (with J. Parkinson and C. Schwer) preprint 2008, arXiv:0801.0709, appeared Journal of Algebra 321 (2009) 3469-3493, doi:10.1016/j.jalgebra.2008.04.015.

(18) Commuting families in Hecke and Temperley-Lieb algebras, (with T. Halverson and M. Mazzocco) preprint 2007, arXiv:0710.0596, appeared in Nagoya Math. J. 195 (2009), 125-152.

  • Halverson-Mazzocco-Ram Abstract
  • Halverson-Mazzocco-Ram Section 1: Introduction
  • Halverson-Mazzocco-Ram Section 2: Affine braid groups, Hecke and Temperley-Lieb algebras
  • Halverson-Mazzocco-Ram Section 3: Schur functors
  • Halverson-Mazzocco-Ram Section 4: Eigenvalues
  • Halverson-Mazzocco-Ram References

(17) Alcove walks, Hecke algebras, spherical functions, crystals and column strict tableaux, preprint 2005, arXiv:0601.343, appeared in Pure and Applied Mathematics Quarterly 2 no. 4 (Special Issue: In honor of Robert MacPherson, Part 2 of 3) (2006) 963-1013.

  • Ram: MacPherson volume paper section 2: Affine Weyl group
  • Ram: MacPherson volume paper section 3: Affine Hecke algebra
  • Ram: MacPherson volume paper section 4: Satake, Hall-Littlewood, and Schwer's formulas
  • Ram: MacPherson volume paper section 5.1: Schur functions, Weyl dimension formula and multiplicities
  • Ram: MacPherson volume paper sections 5.2 and 5.3: Paths and i-strings
  • Ram: MacPherson volume paper section 5.4: Highest weight paths
  • Ram: MacPherson volume paper sections 5.5 and 5.6: Root operators
  • Ram: MacPherson volume paper section 5.7: Column strict tableaux

(16) Affine Hecke algebras and the Schubert calculus, (with S. Griffeth), preprint 2003, arXiv:0405333, appeared in European J. of Combinatorics, Special Volume in honor of Alain Lascoux on the occasion of his 60th birthday, 25 8 (2004) 1263-1283.

  • Griffeth-Ram Section 0: Abstract, Introduction and Acknowledgments
  • Griffeth-Ram Section 1: Preliminaries
  • Griffeth-Ram Section 2: The ring KT(G/B)
  • Griffeth-Ram Section 3: Pieri-Chevalley formulas
  • Griffeth-Ram Section 4: Converting to HT(G/B)
  • Griffeth-Ram Section 5: Rank two and a positivity conjecture

(15) Partition algebras, (with T. Halverson), preprint 2003, arXiv:0401314, appeared in European J. of Combinatorics, 26 (2005) 869-921.

  • Halverson-Ram Partition algebras Section 0: Abstract, Introduction and Acknowledgments
  • Halverson-Ram Partition algebras Section 1: The partition monoid
  • Halverson-Ram Partition algebras Section 2: Partition algebras
  • Halverson-Ram Partition algebras Section 3: Schur-Weyl duality for partition algebras
  • Halverson-Ram Partition algebras Section 4: The basic construction
  • Halverson-Ram Partition algebras Section 5: Semisimple algebras

(14) Kostka-Foulkes polynomials and Macdonald spherical functions (with K. Nelsen), preprint 2003, arXiv:0401298, Published in Surveys in Combinatorics 2003 , C. Wensley ed., London Math. Soc. Lect. Notes 307 , Cambridge University Press, 2003.

  • Nelsen-Ram: Introduction
  • Nelsen-Ram: The root system and Weyl group
  • Nelsen-Ram: The affine Weyl group
  • Nelsen-Ram: The affine Hecke algebra
  • Nelsen-Ram: Kazhdan-Lusztig Bases
  • Nelsen-Ram: Symmetric and alternating functions and their q-analogues
  • Nelsen-Ram: Satake isomorphism
  • Nelsen-Ram: Orthogonality formulae for Kostka-Foulkes polynomials
  • Nelsen-Ram: Formulae for Kostka-Foulkes polynomials
  • Nelsen-Ram: Charge and a positive formula in type A

(13) Affine braids, Markov traces and the category O (with R. Orellana), preprint 2001, arXiv:0401317, appeared in Proceedings of the International Colloquium on Algebraic Groups and Homogeneous Spaces Mumbai 2004, V.B. Mehta ed., Tata Institute of Fundamental Research, Narosa Publishing House, Amer. Math. Soc. (2007) 423-473. This paper has an additional picture: Figure 1.

  • Orellana-Ram: Introduction
  • Orellana-Ram: Preliminaries on Quantum groups
  • Orellana-Ram: Affine braid group representations and the functors Fλ
  • Orellana-Ram: The Bk-modules Mλ/μ and Lλ/μ
  • Orellana-Ram: Markov traces
  • Orellana-Ram: Examples

(12) Representations of graded Hecke algebras (with C. Kriloff), original preprint 2001. Revised version published in Representation Theory, 6 (2002), 31--69.

  • Kriloff-Ram Section 1: Abstract, Introduction, Acknowledgments
  • Kriloff-Ram Section 2: Preliminaries
  • Kriloff-Ram Section 3: Classification of irreducible representations for rank 2
  • Kriloff-Ram Section 4: Classification of calibrated representations
  • Kriloff-Ram Section 5: Combinatorics of local regions

(11) Classification of graded Hecke algebras for complex reflection groups (with A. Shepler), preprint 2001, arXiv:0209.135, Published in Commentari Mathematici Helvetici, 78 No. 2 (2003), 308-334.

  • Ram-Shepler: Abstract, Acknowledgments
  • Ram-Shepler Section 0: Introduction
  • Ram-Shepler Section 1: Graded Hecke algebras
  • Ram-Shepler Section 2: The classification for reflection groups
  • Ram-Shepler Section 3: The graded Hecke algebras Hgr
  • Ram-Shepler Section 4: Examples
  • Ram-Shepler Section 5: A different graded Hecke algebra for G(r,1,n)
  • Ram-Shepler Section 6: References

(10) Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques (with P. Diaconis), original preprint 2000, arXiv:0401318. Shortened version published in Michigan Mathematical Journal , 48 (2000), 157--190.

(9) Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory (with J. Ramagge), preprint 1999, arXiv:0401322. This paper has additional pictures: Figure 1 , Figure 2 and Figure 3 . Published in A tribute to C.S. Seshadri: Perspectives in Geometry and Representation theory, V. Lakshimibai et al eds., Hindustan Book Agency , New Delhi (2003), 428--466.

  • Ram-Ramagge Section 0: Abstract, Introduction, Acknowledgments
  • Ram-Ramagge Section 1: Algebras with Young tableaux theories
  • Ram-Ramagge Section 2: Representation theory transfer
  • Ram-Ramagge Section 3: Standard Young tableaux, representations and Jucys-Murphy elements
  • Ram-Ramagge Section 4: Affine Hecke algebras of general type
  • Ram-Ramagge Section 5: Where does the homomorphism Φ come from?
  • Ram-Ramagge Appendix: Clifford theory

(8) Calibrated representations of affine Hecke algebras, preprint 1998, arXiv:0401323. These results have been published in Affine Hecke algebras and generalized standard Young tableaux, J. Algebra, 230 (2003), 367--415.

(7) Standard Young tableaux for finite root systems, preprint 1998, arXiv:0401329. These results have been published in Affine Hecke algebras and generalized standard Young tableaux, J. Algebra, 230 (2003), 367--415.

  • Ram - Steinberg volume paper Section 0: Abstract, Introduction and acknowledgments
  • Ram - Steinberg volume paper Section 1: The affine Hecke algebra
  • Ram - Steinberg volume paper Section 2: Affine Hecke algebra modules
  • Ram - Steinberg volume paper Section 3: Classification of calibrated representations
  • Ram - Steinberg volume paper Section 4: The structure of local regions
  • Ram - Steinberg volume paper Section 5: The connection to standard Young tableaux
  • Ram - Steinberg volume paper Section 6: Skew shapes, ribbons, conjugation, etc. in type A
  • Ram - Steinberg volume paper Section 7: The type A, root of unity case
  • Ram - Steinberg volume paper Section 8: Standard tableaux for type C in terms of boxes

(6) Skew shape representations are irreducible, preprint 1998, arXiv:0401326. This paper has additional pictures: Figure 1 and Figure 2a and Figure 2b . Published in Combinatorial and Geometric representation theory , S.-J. Kang and K.-H. Lee eds., Contemp. Math. 325 Amer. Math. Soc. 2003, 161-189.

  • Ram - Skew shape representations are irreducible Section 0: Abstract, Introduction and acknoledgments
  • Ram - Skew shape representations are irreducible Section 1: Affine Hecke algebras of type A
  • Ram - Skew shape representations are irreducible Section 2: Tableau combinatorics
  • Ram - Skew shape representations are irreducible Section 3: Weights and weight spaces
  • Ram - Skew shape representations are irreducible Section 4: Classification and construction of calibrated representations
  • Ram - Skew shape representations are irreducible Section 5: "Garnir relations" and an analogue of Young's natural basis
  • Ram - Skew shape representations are irreducible Section 6: Induction and restriction

(5) Representations of rank two affine Hecke algebras, preprint 1998, arXiv:0401327. Published in "Advances in Algebra and Geometry, University of Hyderabad conference 2001", Ed. C. Musili, Hindustan Book Agency , 2003, 57-91.

  • Ram - Rank two classification paper Section 0: Abstract, Introduction, Acknowledgements
  • Ram - Rank two classification paper Section 1: Definitions and preliminary results
  • Ram - Rank two classification paper Section 2: Classification for A1
  • Ram - Rank two classification paper Section 3: Classification for A1xA1
  • Ram - Rank two classification paper Section 4: Classification for A2
  • Ram - Rank two classification paper Section 5: Classification for C2
  • Ram - Rank two classification paper Section 6: Classification for G2

(4) A Pieri-Chevalley formula for K(G/B), preprint 1998, arXiv:0401332.

  • Pittie-Ram Section 0: Abstract, Introduction and Acknowledgments
  • Pittie-Ram Section 1: Background
  • Pittie-Ram Section 2: The class [OP/B] in K(G/B)
  • Pittie-Ram Section 3: Push-pull operators in K-theory
  • Pittie-Ram Section 4: The Pieri-Chevalley formula
  • Pittie-Ram Section 5: Passage to H*(G/B)

(3) A survey of quantum groups: background, motivation, and results, in "Geometric analysis and Lie theory in mathematics and physics'', A. Carey and M. Murray eds., Australian Math. Soc. Lecture Notes Series, 11 Cambridge University Press, 1997, pp. 20-104. MR1690844

  • Adelaide Quantum group notes -1: Contents
  • Adelaide Quantum group notes 0: Introduction
  • Adelaide Quantum group notes I: Hopf Algebras and quasitriangular Hopf algebras
  • Adelaide Quantum group notes II: Lie Algebras and Enveloping Algebras
  • Adelaide Quantum group notes III: Deformations of Hopf algebras
  • Adelaide Quantum group notes IV: Perverse Sheaves
  • Adelaide Quantum group notes V: Quantum Groups
  • Adelaide Quantum group notes VI: Modules for quantum groups
  • Adelaide Quantum group notes VII: Properties of quantum groups
  • Adelaide Quantum group notes VIII: Hall Algebras
  • Adelaide Quantum group notes IX: Link invariants from quantum groups

(2) Combinatorial Representation Theory (with H. Barcelo), preprint 1997, arXiv:9707.221. Published in New perspectives in algebraic combinatorics (Berkeley, CA, 1996--97) , Math. Sci. Res. Inst. Publ., 38 , Cambridge Univ. Press, Cambridge, 1999, pp. 23--90.

  • Complete Survey
  • Section -1: Contents
  • Section -0.5: Abstract
  • Section 0: Introduction
  • Part I Section 1: What is Combinatorial Representation Theory?
    • What is Representation Theory?
    • Main questions in Representation Theory
    • Answers should be of the form ...
  • Part I Section 2: Answers for Sn, the symmetric group
  • Part I Section 3: Answers for GL(n,ℂ), the general linear group
  • Part I Section 4: Answers for finite-dimensional complex semisimple Lie algebras 𝔤
  • Part II Section 5: Generalizing the Sn results
  • Part II Section 6: Generalizations of GL(n, ℂ) results
    • Partial results for further generalizations
  • Appendix A Section A1: Basic representation theory
  • Appendix A Section A2: Partitions and tableaux
  • Appendix A Section A3: The flag variety, unipotent varieties and Springer theory for GL(n, ℂ)
  • Appendix A Section A4: Polynomial and rational representations of GL(n,ℂ)
  • Appendix A Section A5: Schur-Weyl duality and Young symmetrizers
  • Appendix A Section A6: The Borel-Weil-Bott construction
  • Appendix A Section A7: Complex semisimple Lie algebras
  • Appendix A Section A8: Roots, weights and paths
  • Appendix B Section B1: Coxeter groups, groups generated by reflections, and Weyl groups
  • Appendix B Section B2: Complex reflection groups
    • Partial results for G(r,1,n)
  • Appendix B Section B3: Hecke algebras and "Hecke algebras" of Coxeter groups
  • Appendix B Section B4: "Hecke algebras" of the groups G(r,p,n)
  • Appendix B Section B5: The Iwahori-Hecke algebras Hk(q) of type A
    • Partial results for Hk(q)
  • Appendix B Section B6: The Brauer algebras Bk(x)
    • Partial results for Bk(x)
  • Appendix B Section B7: The Birman-Murakami-Wenzl algebras BMWk(r,q)
    • Partial results for BMWk(r,q)
  • Appendix B Section B8: The Templerley-Lieb algebras TLk(x)
    • Partial results for TLk(x)
  • Appendix B Section B9: Complex semisimple Lie groups
  • Section 4: Symplectic and orthogonal higher Casimir elements
  • Section 4: Symplectic and orthogonal higher Casimir elements

(2) A ribbon Hopf algebra approach to the irreducible representations of centralizer algebras: The Brauer, Birman-Wenzl, and Type A Iwahori-Hecke algebras (with R. Leduc), Advances in Math. 125 (1997), 1-94. MR1427801

  • Section -1: Abstract
  • Section -2: Acknowledgements
  • Section 0: Introduction
  • Section 1: Path algebras and tensor power centralizer algebras
  • Section 2: Quasitriangular Hopf algebras, ribbon Hopf algebras and quantum groups
  • Section 3: Ribbon Hopf algebras, conditional expectations and Markov traces
  • Section 4: Centralizer algebras of tensor powers of Vω1, Type Ar
  • Section 5: Centralizer algebras of tensor powers of V=Λω1, Type Br
  • Section 6: Irreducible representations of the Iwahori-Hecke algebras of type A, the Birman-Wnenzl algebras, and the Brauer algebras
  • Appendix
  • References

(2) Standard Lyndon bases of Lie algebras and enveloping algebras (with P. Lalonde), Trans. of the Amer. Math. Soc. 347 (1995), 1821-30. MR1273505

  • Section -1: Abstract
  • Section 1: Lyndon words and the free Lie algebra
  • Section 2: Standard bases
  • Section 3: Finite dimensional simple Lie algebras
  • References

(1) Weyl group symmetric functions and the representation theory of Lie algebras, Proceedings of the 4th conference "Formal Power Series and Algebraic Combinatorics", Publ. LACIM 11 (1992), 327-342.

  • Section 0: Introduction
  • Section 1: Classical symmetric functions
  • Section 2: Weyl group symmetric functions
  • Section 3: Representation theory
  • Section 4: Centralizer algebras
  • Section 5: Orthogonality

(0) Dissertation Chapter 1, Unpublished chapter of Ph.D. Thesis

  • Dissertation Chapter 1: Abstract
  • Dissertation Chapter 1: §1 Representations
  • Dissertation Chapter 1: §2 Finite dimensional algebras
  • Dissertation Chapter 1: §3 Semisimple algebras
  • Dissertation Chapter 1: §4 Double Centralizer nonsense
  • Dissertation Chapter 1: §5 Induction and restriction