Some Non-Trivial Kazhdan-Lusztig Coefficients of an Affine Weyl Group of Type $\tilde A_n$

Details Some Non-Trivial Kazhdan-Lusztig Coefficients of an Affine Weyl Group of Type $\tilde A_n$ Some Non-Trivial Kazhdan-Lusztig Coefficients of an Affine Weyl Group of Type $\tilde A_n$

2009-09-18

arxiv.org/abs/0909.3394v4

Mathematics

Representation Theory

19 pages, to appear in SCIENCE CHINA Mathematics

Scientific paper

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.

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