Some Non-Trivial Kazhdan-Lusztig Coefficients of an Affine Weyl Group of Type ${\tilde{A}}_n$

Abstract

In this paper we show that the leading coefficient $\mu (y,w)$ of some Kazhdan-Lusztig polynomials $P_{y,w}$ with $y,w$ in an affine Weyl group of type ${\tilde{A}}_n$ is $n+2$. This fact has some consequences on the dimension of first extension groups of finite groups of Lie type with irreducible coefficients.

arXiv comment19 pages, to appear in SCIENCE CHINA Mathematics

References in corpus (2)

• The leading coefficient of certain Kazhdan-Lusztig polynomials of the permutation group $S_n$
• Leading coefficients of the Kazhdan-Lusztig polynomials for an Affine Weyl group of type $\widetilde{B_2}$

Cited by in corpus (5)

• Lusztig's $a$-function for Coxeter groups with complete graphs
• Blocks of the category ${\mathcal{O}}^{\mathfrak{p}}$ in type $E$
• Janzten coefficients and Blocks of category ${\mathcal{O}}^{\mathfrak{p}}$
• Cohomological growth rates and Kazhdan-Lusztig polynomials
• Bounding Ext for modules for algebraic groups, finite groups, and quantum groups