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 Advanced Studies in Pure Mathematics 2001; 422 pp; hardcover Volume: 28 ISBN-10: 4-314-10141-5 ISBN-13: 978-4-314-10141-7 Order Code: ASPM/28 This volume is a collection of papers written by the speakers of two international conferences held at the Research Institute for Mathematical Sciences (RIMS) at Kyoto University (Japan). Included are articles and surveys treating representations of (affine) Hecke algebras and affine Lie algebras, combinatorial properties of Kazhdan-Lusztig polynomials, crystals and Gelfand-Zetland bases for Lie (super) algebras, etc. Volumes in this series are freely available electronically 5 years post-publication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students and research mathematicians interested in combinatorics. Table of Contents S. Ariki -- Robinson-Schensted correspondence and left cells G. Benkart and S.-J. Kang -- Crystal bases for quantum superalgebras F. Brenti -- Approximation results for Kazhdan-Lusztig polynomials M. Ciucu and C. Krattenthaler -- Plane partitions II: $$5\tfrac{1}{2}$$ symmetry classes A. Gyoja, K. Nishiyama, and K. Taniguchi -- Invariants for representations of Weyl groups, two-sided cells, and modular representations of Iwahori-Hecke algebras G. Hatayama, Y. Koga, A. Kuniba, M. Okado, and T. Takagi -- Finite crystals and paths M. Ishikawa and M. Wakayama -- Minor summation formulas of Pfaffians, survey and a new identity A. Kirillov, Jr. and A. Lascoux -- Factorization of Kazhdan-Lusztig elements for Grassmanians B. Leclerc and J.-Y. Thibon -- Littlewood-Richardson coefficients and Kazhdan-Lusztig polynomials A. I. Molev -- A weight basis for representations of even orthogonal Lie algebras T. Nakajima and H.-F. Yamada -- Schur's $$Q$$-functions and twisted affine Lie algebras M. Nazarov -- Capelli elements in the classical universal enveloping algebras Y. Roichman -- On permutation statistics and Hecke algebra characters A. Schilling and M. Shimozono -- Bosonic formula for level-restricted paths T. Shoji -- Length functions for $$G(r,p,n)$$ T. Suzuki -- Representations of degenerate affine Hecke algebra and $$\mathfrak{gl}_n$$ H. Tagawa -- A recursion formula of the weighted parabolic Kazhdan-Lusztig polynomials Y. Yamada -- Special polynomials and generalized Painlevé equations M. Yamaguchi -- A duality of a twisted group algebra of the hyperoctahedral group and the queer Lie superalgebra