Kazhdan-Lusztig polynomials for $\tilde{B}_2$

Karina Batistelli, Aram Bingham, David Plaza

Published 2021-02-02Version 1

Kazhdan and Lusztig define, for an arbitrary Coxeter system $(W,S)$, a family of polynomials indexed by pairs of elements of $W$. Despite their relevance and elementary definition, the explicit computation of these polynomials is still one of the hardest open problems in algebraic combinatorics. In this paper we explicitly compute Kazhdan-Lusztig polynomials for a Coxeter system of type $\tilde{B}_2$.