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We provide combinatorial rules to compute Kazhdan--Lusztig polynomials for the Hermitian symmetric pair $(B_N,A_{N-1})$ when the Hecke algebra has unequal parameters.
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H. Saleur, Virasoro and Temperley Lieb algebras , Knots, topology and quantum field theories (Florence, 1989), World Sci. Publ., River Edge, NJ, 1989, pp. 485–496
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A. Kirillov, Jr. and A. Lascoux, Factorization of Kazhdan–Lusztig elements for Grassmannians , Combinatorial methods in representation theory (Kyoto, 1998), Adv. Stud. Pure. Math., vol. 28, Kinokuniya, Tokyo, 2000, pp. 143–154, [ arXiv:math/9902072 ]
2000
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F. Brenti, Kazhdan–Lusztig and R R -polynomials, Young’s lattice, and Dyck partitions , Pacific Journal of Mathematics 207
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G. Lusztig, Hecke Algebra with Unequal Parameters , CRM monograph series, vol. 18, American Mathematical Society, 2003
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by same author, Parabolic Kazhdan–Lusztig polynomials for Hermitian symmetric spaces , Trans. Amer. Math. Soc. 361
2009
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P. Martin, Temperley–Lieb algebras and the long distance properties of statistical mechanical models , J. Phys. A 23
1990
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2010
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2012
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