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Littlewood-Richardson coefficients and Kazhdan-Lusztig polynomials. (English) Zbl 1058.20006
Koike, Kazuhiko (ed.) et al., Combinatorial methods in representation theory. Papers of the conference on combinatorial methods in representation theory, July 21–July 31, 1998 and the conference on interaction of combinatorics and representation theory, October 26–November 6, 1998, Kyoto, Japan. Tokyo: Kinokuniya Company Ltd. (ISBN 4-314-10141-5/hbk). Adv. Stud. Pure Math. 28, 155-220 (2000).
Summary: We show that the Littlewood-Richardson coefficients are values at 1 of certain parabolic Kazhdan-Lusztig polynomials for affine symmetric groups. These \(q\)-analogues of Littlewood-Richardson multiplicities coincide with those previously introduced by A. Lascoux, B. Leclerc and J.-Y. Thibon [J. Math. Phys. 38, No. 2, 1041-1068 (1997; Zbl 0869.05068)] in terms of ribbon tableaux.
For the entire collection see [Zbl 0963.00024].

MSC:
20C08 Hecke algebras and their representations
33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
20C30 Representations of finite symmetric groups
05E10 Combinatorial aspects of representation theory
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