Abstract
In 1979 Kazhdan and Lusztig defined, 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 B˜2.
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