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$ D$-sets and BG-functors in Kazhdan-Lusztig theory

Author: Yi Ming Zou
Journal: Proc. Amer. Math. Soc. 123 (1995), 935-943
MSC: Primary 22E47; Secondary 17B35
MathSciNet review: 1242113
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Abstract: By using Deodhar's combinatorial setting and Bernstein-Gelfand projective functors, this paper provides some necessary and sufficient conditions for a highest weight category to have a Kazhdan-Lusztig theory. A consequence of these conditions is that in the semisimple Lie algebra case, the Kazhdan-Lusztig conjecture on the multiplicities of a Verma module implies the nonnegativity conjecture on the coefficients of Kazhdan-Lusztig polynomials.

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Keywords: D-sets, BG-functors
Article copyright: © Copyright 1995 American Mathematical Society

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