Oeuvres Arun Ram |
School of Mathematics and Statistics University of Melbourne Parkville VIC 3010 Australia aram@unimelb.edu.au |
In the internet age, the notion of "publication" dramatically changes avatar. In keeping with these advances, this page is now titled "Oeuvres" and lists polished and completed full length works where I am among the authors and the works are publicly presented. Included are works published on YouTube, on the arXiv, and other venues.
(11) Ian G. Macdonald: Works of Art, presented at FPSAC 2024 Bochum, Germany, in Sém. Lothar. Combin. 91B (2024), Art. 0, 26 pp., arxiv2408.01704., published on YouTube.
(10) Remembering Georgia Benkart (with Alejandro Adem, Tom Halverson, Efim Zelmanov), Notices of the American Mathematical Society 70 No. 3, March 2023, DOI:https://doi.org/10.1090/noti2653.
(9) Gems from the work of Georgia Benkart (with Tom Halverson), Notices of the American Mathematical Society 69 No. 3, March 2022, DOI:https://doi.org/10.1090/noti2447.
(8) Maybe I could be a Mathematician: A story of growing up alongside vinyl, CD, MP3 and YouTubeRed, a public lecture presented by The Institute for Enquiring Minds, 31 July 2018, published on YouTube.
(7) The glass bead game, Public Lecture as part of the BrisScience series at The EDGE, Brisbane, 7 July 2015, published on YouTube.
(6) Is my daughter a genius? Managing the education of a child with Down Syndrome, a paper presented at the conference Honoring the Child, Honoring Equity: Embracing diverse identities" held at the University of Melbourne Graduate School of Education 21-22 November 2014. These slides were used for the lecture.
(5) D-N. Verma (1933-2012), A Memory, published in Mathematics Newsletter of the Ramanujan Mathematical Society, November 2012.
(4) Millennium Prize: the Hodge Conjecture, published in The Conversation http://theconversation.edu.au/millenium-prize-the-hodge-conjecture-4243, 22 November 2011.
(3) Oberwolfach report No. 15/2010 Combinatorial Representation Theory, organized and reported by C. Bessenrodt, F. Brenti, A. Kleshchev and A. Ram, 21-27 March 2010, DOI: 10.4171/OWR/2010/15
(2) MathML for mathematics research articles (flexible version), stable version, pdf version, preprint 2008.
(1) A review of Young tableaux: With applications to representation theory and geometry, by William Fulton, Cambridge University Press, New York, 1997. Bulletin American Math. Soc. 36 (1999), 251-259.
(66)
c-functions and Koornwinder polynomials
(with Laura Colmenarejo)
In memory of Ian G. Macdonald,
arXiv2410.19957
(65)
Lusztig varieties and Macdonald polynomials
Dedicated to Peter Littelmann
Algebra and Representation Theory
https://doi.org/10.1007/s10468-024-10305-6
arXiv:2402.17935.
(64)
Clebsch-Gordan coefficients for Macdonald polynomials
(with Aritra Bhattacharya)
Algebra and Representation Theory 27 (2024) 2423–2464.
https://doi.org/10.1007/s10468-024-10303-8
arXiv2310.10846.
(63)
c-functions and Macdonald polynomials
(with Laura Colmenarejo)
In memory of Georgia Benkart,
J. Algebra 655 (2024), 163-222, MR4756469
arXiv2212.03312.
(62)
Set-valued tableaux for Macdonald polynomials
(with Zajj Daugherty)
In memory of Georgia Benkart,
Sém. Lothar. Combin. 89B (2023), Art. 42, 12 pp., MR4659550.
arXiv2212.04033.
(61)
Monk rules for type GLn Macdonald polynomials
(with Tom Halverson)
In memory of Georgia Benkart,
J. Algebra 655 (2024), 493-516, MR4756478.
arXiv2212.04032.
(60) Double coset Markov chains, (with Persi Diaconis and Mackenzie Simper) Forum of Mathematics, Sigma, Volume 11 e2 (2023), DOI: https://doi.org/10.1017/fms.2022.106, arXiv2208.10699.
(59)
Comparing formulas for type GLn Macdonald polynomials,
and
Supplement (with Weiying Guo)
dedicated to Hélène Barcelo,
Algebraic Combinatorics (ALCO),5 (2022) 849-883 and 885-923,
DOI: 10.5802/alco.227
and DOI: 10.5802/alco.228.
arXiv2104.02942 and
arXiv2104.04578.
(58)
Calibrated representations of two boundary Temperley-Lieb algebras,
(with Zajj Daugherty) in memory of Vladimir Rittenberg (1934-2018),
Annals of Representation Theory 2 (2025) 405-438.
arXiv2009.02812.
(57)
Positive level, negative level and level zero,
(with Finn McGlade and Yaping Yang),
appeared in the special volume in conjuction with the conference
International Festival in Schubert Calculus, Sun-Yat Sen University,
Guangzhou China, 5-11 November 2017,
Schubert calculus and its applications in combinatorics and
representation theory,
Springer Proc. Math. Stat. 332, Springer,
Singapore (2020) 153-194, MR4167516,
arXiv1907.11796.
(56)
The Steinberg-Lusztig tensor product theorem, Casselman-Shalika and
LLT polynomials, (with M. Lanini),
Representation Theory 23 (2019) 188-204
DOI: https://doi.org/10.1090/ert/524
.
arXiv1804.03710,
(55)
A Fock space model for decomposition numbers for quantum groups at roots of
unity,
(with M. Lanini and Paul Sobaje),
Kyoto J. Math 59 Number 4 (2019), 955-991
DOI:10.1215/21562261-2019-0033.
arXiv1612.03120,
(54)
Two boundary Hecke algebras and combinatorics of type C,
(with Z. Daugherty),
Annals of Representation Theory 2 (2025) 355-404.
arXiv1804.10296.
(53)
The thickness of Schubert cells as incidence structures,
(with J. Bamberg and J. Xu),
Journal of the Australian Mathematical Society 109
(2020) 145 - 156.
DOI: https://doi.org/10.1017/S1446788719000363
arXiv1804.03864.
(52)
Cyclic representations of the periodic Temperley Lieb algebra, complex Virasoro representations
and stochastic processes,
(with F.C. Alcaraz and V. Rittenberg),
J. Phys. A: Math Theor. 47 (2014) 212003.
http://stacks.iop.org/1751-8121/47/212003
MR3206121,
arXiv1402.5990,
(51)
Generalized Schubert Calculus, (with N. Ganter),
arXiv1212.5742,
J. Ramanujan Math. Soc. 28A
(Special Issue-2013), 149-190.
MR3115192,
(50)
Hopf algebras and Markov chains: Two examples and a theory,
(with P. Diaconis and A. Pang),
arXiv1206.3620,
Journal of Algebraic Combinatorics 39 (2014) 527-585
http://dx.doi.org/10.1007/s10801-013-0456-7.
MR3183482,
(49)
Affine and degenerate affine BMW algebras: Actions on tensor space
(with Z. Daugherty and R. Virk),
arXiv1205.1852,
Selecta Mathematica 19 no. 2 (2013) 611-653.
MR3090238
(48)
Symmetry breaking, subgroup embeddings and the Weyl group
(with D. George, J. Thompson and R. Volkas),
arXiv1203.1048,
Physical Review D 87 105009 (2013) [14 pages]
http://prd.aps.org/abstract/PRD/v87/i10/e105009.
(47)
Affine and degenerate affine BMW algebras: The center
(with Z. Daugherty and R. Virk),
arXiv1105.4207,
Osaka J. Math 51 (2014), 257-283.
MR3192543,
(46)
Universal Specht modules for cyclotomic Hecke algebras
(with A. Kleshchev and A. Mathas),
arXiv1102.3519,
Proc. London Math. Soc. (3) 105 (2012) 1245-1289.
MR3004104
(45)
A probabilistic interpretation of the Macdonald polynomials (with P. Diaconis),
made public 2010 arXiv1007.4779,
The Annals of Probability 40 (2012) Vol. 40 No. 5, 1861-1896, DOI 10.1214/11-AOP674,
MR3025704,
(44)
Universal Verma modules and the Misra-Miwa Fock space
(with P. Tingley),
made public 2010 arXiv1002.0558,
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,
MR2753641
(43)
Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words (with A. Kleshchev),
made public 2009 arXiv0909.1984,
Math. Ann. 349 (2011), 943-975, DOI 10.1007/s00208-010-0543-1,
MR2777040
(42)
Homogeneous representations of Khovanov-Lauda algebras
(with A. Kleshchev),
made public 2008 arXiv0809.0557,
J. Eur. Math. Soc. 12 (2010), 1293-1306, DOI 10.4171/JEMS/230,
MR2677617
(41)
Alcove walks, buildings, symmetric functions and representations
(with J. Parkinson),
made public 2008 arXiv0807.3602.
To my knowledge, THIS PAPER HAS AN ERROR IN THE THIRD PARAGRAPH OF THE PROOF OF LEMMA 3.1. I think the statement is correct but, as is, the proof is not.
(40)
A combinatorial formula for Macdonald polynomials (with M. Yip),
made public 2008 arXiv0803.1146,
Adv. Math. 226 (2011), 309-331, doi:10.1016/j.aim.2010.06.022,
MR2735761
(39)
Combinatorics in affine flag varieties,
(with J. Parkinson and C. Schwer),
made public 2008 arXiv:0801.0709,
J. of Algebra 321 (2009) 3469-3493,
doi:10.1016/j.jalgebra.2008.04.015,
MR2510057
(38)
Commuting families in Hecke and Temperley-Lieb algebras
(with T. Halverson and M. Mazzocco),
made public 2007 arXiv:0710.0596,
Nagoya Math. J. 195 (2009), 125-152,
MR2552957
(37)
Alcove walks, Hecke algebras, Spherical functions, crystals and column strict tableaux,
made public 2006, arXiv:0601.343,
Pure and Applied Mathematics Quarterly 2 no. 4
(Special Issue: In honor of Robert MacPherson, Part 2 of 3)
(2006) 963-1013. MR2282411
(36)
Affine Hecke algebras and the Schubert calculus
(with S. Griffeth),
preprint 2003, arXiv:0405333
European J. of Combinatorics, Special Volume in
honor of Alain Lascoux on the occasion of his 60th birthday,
25 8 (2004) 1263-1283. MR2095481
(35)
Partition algebras
(with T. Halverson),
preprint 2003, arXiv:0401314
European J. of Combinatorics,
26 (2005) 869-921. MR2143201
(34)
Kostka-Foulkes polynomials and Macdonald spherical functions
(with K. Nelsen),
preprint 2003, arXiv:0401298
in
Surveys in Combinatorics 2003 , C. Wensley ed.,
London Math. Soc. Lect. Notes 307 ,
Cambridge University Press, 2003, 325--370.
MR2011741.
(33)
Affine Braids, Markov traces and the category O,
(with R. Orellana),
This paper has an additional picture:
Figure 1.
preprint 2001, arXiv:0401317
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.
MR2348913
(32)
Representations of graded Hecke algebras
(with C. Kriloff),
original preprint 2001,
revised 2002
Representation Theory 6 (2002), 31--69.
MR1915086
(31)
Classification of graded Hecke algebras for complex reflection groups
(with A. Shepler),
preprint 2001, arXiv:0209.135
Commentari Mathematici Helvetici, 78 No. 2 (2003), 308-334.
MR1988199
(30)
In memory of Sergei Kerov 1946-2000:
preprint 2000, arXiv:0401330.
q-rook monoid algebras, Hecke algebras and Schur-Weyl duality
(with T. Halverson),
Zapiski Nauchanyh Seminarov POMI , 283 (2001),
224-250 and
Journal of Mathematical Sciences, 121 No. 3 (2004),
2419-2436. MR1879072.
(29)
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.
MR1786485
(28)
Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory
(with J. Ramagge),
This paper has additional pictures:
Figure 1 ,
Figure 2
and
Figure 3 .
preprint 1999, arXiv:0401322.
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. MR2017596
(27)
Affine Hecke algebras and generalized standard Young tableaux,
This paper is a revised and combined version of the 1998 preprints
arXiv:0401323
and
arXiv:0401329.
Special issue celebrating the 80th birthday of Robert Steinberg, J. Algebra, 230 (2003), 367--415.
MR1976700.
(26)
Calibrated representations of affine Hecke algebras,
preprint 1998, arXiv:0401323.
A revised version of these results has been published in
Affine Hecke algebras and generalized standard Young tableaux,
J. Algebra, 230 (2003), 367--415.
(25)
Standard Young tableaux for finite root systems,
preprint 1998, arXiv:0401329.
A revised version of these results has been published in
Affine Hecke algebras and generalized standard Young tableaux,
J. Algebra, 230 (2003), 367--415.
(24)
Skew shape representations are irreducible,
This paper has additional pictures:
Figure 1
and
Figure 2a
and
Figure 2b ,
preprint 1998, arXiv:0401326,
in Combinatorial and Geometric representation theory ,
S.-J. Kang and K.-H. Lee eds., Contemp. Math. 325
Amer. Math. Soc. 2003, 161-189. MR1988991
(23)
Representations of rank two affine Hecke algebras,
preprint 1998, arXiv:0401327
in "Advances in Algebra and
Geometry, University of Hyderabad conference 2001", C. Musili ed.,
Hindustan Book Agency , 2003, 57-91.
MR1986143
(22)
A Pieri-Chevalley formula for K(G/B) (with H. Pittie),
preprint 1998, arXiv:0401332
(21)
A Pieri-Chevalley formula in the K-theory of a G/B-bundle (with H. Pittie),
preprint 1998, arXiv:0401331
Electronic Research Announcements 5 (1999), 102--107.
MR1701888
(20)
Combinatorial Representation Theory
(with H. Barcelo),
preprint 1997 arXiv:math/9707221,
in New perspectives in algebraic combinatorics
(Berkeley, CA, 1996--97) , 23--90,
Math. Sci. Res. Inst. Publ. 38 ,
Cambridge Univ. Press, Cambridge, 1999, pp. 23--90. MR1731814
(19) Bitraces for GL_n(F_q) and the Iwahori-Hecke algebra of type A (with T. Halverson),
an additional table of values of the bitrace for n=6 is available,
Table 1 .
Indag. Mathem., N.S.
10 (1999), 247-268.
MR1816219.
(18)
Explicit irreducible representations of the Iwahori-Hecke algebra of
type F_4 (with D. Taylor),
preprint 1996 arXiv:math/9703210,
manuscripta mathematica 99 (1999), 13-37.
MR1697201
(17)
Tensor product representations for orthosymplectic Lie superalgebras
(with G. Benkart and C.-Y. Lee Shader),
preprint 1995 arXiv:math/9607232,
J. Pure and Applied Algebra 130 (1998), 1-48.
MR1632811
(16)
Seminormal representations of Weyl groups and Iwahori-Hecke algebras,
preprint 1995 arXiv:math/9511223.
(16)
Murnaghan-Nakayama rules for ``Hecke algebras'' of the
complex reflection groups G(r,p,n) (with T. Halverson),
preprint 1995 arXiv:math/9511222,
Canadian Journal of Mathematics.
50 (1998), 167-192. MR1618815
(15)
Robinson-Schensted-Knuth insertion and characters of symmetric groups and Iwahori-Hecke algebras of type A
preprint 1996 arXiv:math/9607231,
Published under the title "An elementary proof of Roichman's rule for irreducible characters of
Iwahori-Hecke algebras of type A",
in Mathematical essays in honor of Gian-Carlo Rota B. Sagan and R. Stanley ed., Birkhauser, Boston 1998, pp. 335-342. MR1627307
(14)
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
(13)
A "second orthogonality relation'' for
characters of Brauer algebras,
European J. of Combinatorics, 18 (1997), 685-706.
MR1468338
(12)
Seminormal representations of Weyl groups and Iwahori-Hecke algebras,
Proceedings of the London Math. Soc. (3)
75 (1997), 99-133. MR1444315
(11)
Iwahori-Hecke algebras of type A, bitraces and symmetric
functions (with T. Halverson and R. Leduc),
Int. Math. Research Notices (1997)
No. 9, 401-416. MR1443319
(10) Applications of the Frobenius formulas for the characters of the symmetric group and the Hecke algebras of type A (with J. Remmel), J. of Algebraic Combinatorics 6 (1997), 59-87. MR1431825
(9) 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
(8)
Murnaghan-Nakayama rules for characters
of Iwahori-Hecke algebras of classical Type (with T. Halverson),
Trans. of Amer. Math. Soc. 348 (1996), 3967-3995.
MR1322951
(7)
Combinatorics of the q-basis of symmetric functions (with J. Remmel and S.T. Whitehead),
J. Combinatorial Theory Ser. A. 76 (1996) 231-71. MR1416016
(6)
Characters of algebras containing a Jones basic construction:
The Temperley-Lieb, Okada, Brauer, and Birman-Wenzl algebras (with T. Halverson),
Advances in Math. 116 (1995) 263-321. MR1363766
(5)
Standard Lyndon bases of Lie algebras and enveloping algebras (with P. Lalonde),
Trans. of the Amer. Math. Soc.
347 (1995), 1821-30. MR1273505
(4)
Characters of Brauer's centralizer algebras,
Pacific Journal of Math.
169
(1995) 173-200. MR1346252
(3)
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.
(2)
Matrix units for centralizer algebras (with H. Wenzl),
J. of Algebra
145 (1992), 378-395. MR1144939
(1)
A Frobenius formula for the Characters of the Hecke algebras,
Invent. Math.
106
(1991), 461-488. MR1134480
(0)
Dissertation Chapter 1,
Chapter of University of California San Diego Ph.D. Thesis 1991.