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

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arxiv 2102.01278 v1 pith:QDJGH6ZE submitted 2021-02-02 math.RT math.CO

Karina Batistelli , Aram Bingham , David Plaza This is my paper · ORCID
classification math.RTmath.CO
keywords polynomialscoxeterkazhdan-lusztigsystemtildealgebraicarbitrarycombinatorics
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abstract

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 $\tilde{B}_2$.

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  1. Growth in affine Hecke categories

    math.RT 2026-08 accept novelty 7.0 of 10

    In affine Hecke categories, high tensor powers of a fixed object have a number of indecomposable summands of order n^{-|Phi^+|/2} times an exponential; proved in type A1, and for longest elements in type A2, with coar...

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