Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

Hecke algebra characters and immanant conjectures

Author(s): Mark Haiman
Journal: J. Amer. Math. Soc. 6 (1993), 569-595.
MSC: Primary 05E05; Secondary 14M15, 20C30, 20F55
MathSciNet review: 1186961
Retrieve article in: PDF
This article is available free of charge

References | Similar articles | Additional information

References:

[1]
D. Barbasch and D. Vogan, Primitive ideals and orbital integrals in complex exceptional groups. J. Algebra 80 (1983), 350-382. MR 691809 (84h:22038)

[2]
A. Beilinson and J. Bernstein, Localisation des $ g$-modules. C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), 15-18. MR 610137 (82k:14015)

[3]
A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers. Astérisque 100 (1983). MR 751966 (86g:32015)

[4]
N. Bourbaki, Groupes et algebras de Lie, Chapitres 4, 5, 6, Hermann, Paris, (1968). MR 0240238 (39:1590)

[5]
F. Brenti, Unimodal polynomials arising from symmetric functions, Proc. Amer. Math. Soc. 108 (1990), 1133-1141. MR 993741 (90g:05016)

[6]
J. Brylinski and M. Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), 387-410. MR 632980 (83e:22020)

[7]
P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. Millett, and A. Ocneanu, A new polynomial invariant of knots and links. Bull. Amer. Math. Soc. 12 (1985), 239-246. MR 776477 (86e:57007)

[8]
M. Goresky and R. MacPherson, Intersection homology. II, Invent. Math. 72 (1983), 77-129. MR 696691 (84i:57012)

[9]
I. Goulden and D. Jackson, Immanants of combinatorial matrices, J. Algebra 148 (1992), 305-324. MR 1163738 (93i:05132)

[10]
C. Greene, Proof of a conjecture on immanants of the Jacobi-Trudi matrix, Linear Algebra Appl. 171 (1992), 65-79. MR 1165445 (93i:05133)

[11]
N. Jacobson, Lie algebras, Interscience, New York, 1962. MR 0143793 (26:1345)

[12]
J. Jantzen, Moduln mit einem höchsten Gewicht, Lecture Notes in Math., vol. 750, Springer-Verlag, Berlin, Heidelberg, and New York, 1979. MR 552943 (81m:17011)

[13]
M. Jimbo, A $ q$-analogue of $ U(gl(N + 1))$, Hecke algebra, and the Yang-Baxter equation, Lett. Math. Physics 11 (1986), 247-252. MR 841713 (87k:17011)

[14]
V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987), 335-388. MR 908150 (89c:46092)

[15]
-, Index for subfactors. Invent. Math., 72 (1983) 1-25. MR 696688 (84d:46097)

[16]
A. Joseph, Towards the Jantzen conjecture. III, Compositio Math. 41 (1981), 23-30. MR 594481 (81m:17013b)

[17]
D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184. MR 560412 (81j:20066)

[18]
-, Schubert varieties and Poincaré duality, Proc. Sympos. Pure Math., vol. 36, Amer. Math. Soc., Providence, RI, 1980, pp. 185-203. MR 573434 (84g:14054)

[19]
R. C. King and B. G. Wybourne, Characters of Hecke algebras $ {H_n}(q)$ of type $ {A_{n             - 1}}$, J. Physics A 23 (1990), L1193-L1197. MR 1086259 (92d:20011)

[20]
A. Lascoux and M.-P. Schützenberger, Schubert polynomials and the Littlewood-Richardson rule, Lett. Math. Phys. 10 (1985), 111-124. MR 815233 (87g:20021)

[21]
E. Lieb, Proofs of some conjectures on permanents, J. Math. Mech. 16 (1966), 127-134. MR 0202745 (34:2605)

[22]
D. E. Littlewood, The theory of group characters, 2nd ed., Oxford Univ. Press, London, 1950.

[23]
I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Univ. Press, London, 1979. MR 553598 (84g:05003)

[24]
A. Ram, A Frobenius formula for the characters of the Hecke algebras, Invent. Math. 106 (1991), 461-488. MR 1134480 (93c:20029)

[25]
I. Schur, Über endliche Gruppen und Hermitesche Formen, Math. Z. 1 (1918), 184-207. MR 1544291

[26]
M.-P. Schützenberger, La correspondance de Robinson, Combinatoire et Représentation du Groupe Symétrique--Strasbourg, 1976 (D. Foata, ed.), Lecture Notes in Math., vol. 579, Springer-Verlag, Berlin, Heidelberg, and New York, 1977, pp. 59-113. MR 0498826 (58:16863)

[27]
T. A. Springer, Quelques applications de la cohomologie d'intersection, Sém. Bourbaki 589 (1982).

[28]
R. P. Stanley, Log-concave and unimodal sequences in algebra, combinatorics, and geometry, Graph Theory and Its Applications: East and West, Ann. N. Y. Acad. Sci. 576 (1989), 500-535. MR 1110850 (92e:05124)

[29]
R. P. Stanley and J. Stembridge, On immanants of Jacobi-Trudi matrices and permutations with restricted position, J. Combin. Theory Ser. A (to appear). MR 1207737 (94d:05147)

[30]
J. Stembridge, Some conjectures for immanants, Canad. J. Math. 44 (1992), 1079-1099. MR 1186482 (93i:15007)

[31]
-, Eulerian numbers, tableaux, and the Betti numbers of a toric variety, Discrete Math. 99 (1992), 307-320. MR 1158793 (93f:05103)

[32]
-, Immanants of totally positive matrices are non-negative, Bull. London Math. Soc. 23 (1991), 422-428. MR 1141010 (93d:05156)

[33]
J. Vanderjeugt, An algorithm for characters of Hecke algebras $ {H_n}(q)$ of type $ {A_{n             - 1}}$, J. Physics A 24 (1991), 3719-3725. MR 1123644 (92i:05224)

[34]
H. Wenzl, Hecke algebras of type $             {A_n}$ and subfactors, Invent. Math. 92 (1988), 349-383. MR 936086 (90b:46118)

Similar Articles:

Retrieve articles in Journal of the American Mathematical Society with MSC: 05E05, 14M15, 20C30, 20F55

Retrieve articles in all Journals with MSC: 05E05, 14M15, 20C30, 20F55


Additional Information:

DOI: 10.1090/S0894-0347-1993-1186961-9
PII: S0894-0347-1993-1186961-9
Copyright of article: Copyright 1993, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia