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

Zou, Yi Ming

doi:10.1090/S0002-9939-1995-1242113-9

$D$-sets and BG-functors in Kazhdan-Lusztig theory
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Proc. Amer. Math. Soc. 123 (1995), 935-943 Request permission

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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