Poincar\'e series of double coset representatives of Coxeter groups

Gianmarco Chinello

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arXiv · 2010.10796

Poincar\'e series of double coset representatives of Coxeter groups

Gianmarco Chinello

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Abstract

Let $(W,S)$ be a Coxeter system of finite rank and let $J,K\subset S$. We study the rationality of the Poincar\'e series of the set of representatives of minimal length of $(W_J,W_K)$-double cosets of $W$: we conclude that it depends mostly on the rationality of the Poincar\'e series of the normalizers of finite parabolic subgroups of $W$. For affine Weyl groups, we prove that all these series are rational and we give some explicit examples.

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Gianmarco Chinello. 2020-10-21. Poincar\'e series of double coset representatives of Coxeter groups. https://arxiv.org/abs/2010.10796

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