Leading coefficients of the Kazhdan-Lusztig polynomials for an Affine Weyl group of type $\widetilde{B_2}$

Details Leading coefficients of the Kazhdan-Lusztig polynomials for an Affine Weyl group of type $\widetilde{B_2}$ Leading coefficients of the Kazhdan-Lusztig polynomials for an Affine Weyl group of type $\widetilde{B_2}$

2008-05-22

arxiv.org/abs/0805.3463v2

Mathematics

Combinatorics

31 pages

Scientific paper

In this paper we compute the leading coefficients $\mu (u,w)$ of the Kazhdan--Lusztig polynomials $P_{u,w}$ for an affine Weyl group of type $\tilde{B}_2$. By using the \textbf{a}-function of a Coxeter group defined by Lusztig (see [L1, \S2]), we compute most $\mu (u,w)$ explicitly. With part of these values $\mu (u,w)$, we show that a conjecture of Lusztig on distinguished involutions is true for an affine Weyl group of type $\tilde{B}_2$. We also show that the conjectural formula in [L3, (12)] needs a modification.

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