Classifying quotients on Coxeter groups by isomorphism in Bruhat order

Joseph Newton

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arXiv · 2303.06619

Classifying quotients on Coxeter groups by isomorphism in Bruhat order

Joseph Newton

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Abstract

We classify all quotients $W/W_J$ up to isomorphism in Bruhat order, with $(W,S)$ a Coxeter system and $W_J$ a parabolic subgroup of $W$. In particular, the non-trivial isomorphisms fall into a small number of cases which are highly restricted; all have $W$ finite and $W_J$ a maximal parabolic. This has the immediate application of classifying dominant and antidominant blocks of category $\mathcal O$ for Kac-Moody algebras up to equivalence.

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Joseph Newton. 2023-03-12. Classifying quotients on Coxeter groups by isomorphism in Bruhat order. https://arxiv.org/abs/2303.06619

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