Kazhdan-Lusztig coefficients for an Affine Weyl group of type $\widetilde{A_2}$

TL;DR

This paper computes all leading coefficients of Kazhdan-Lusztig polynomials for an affine Weyl group of type A_2, providing a complete set of values for these coefficients.

Contribution

It explicitly determines all leading Kazhdan-Lusztig coefficients for the affine A_2 group, a previously uncalculated case.

Findings

All (u,w) values are explicitly given.

Provides a complete characterization of leading coefficients for A_2.

Enhances understanding of Kazhdan-Lusztig polynomials in affine types.

Abstract

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 $\widetilde{A_2}$. We give all the values $\mu (u,w)$.