Classifying quotients on Coxeter groups by isomorphism in Bruhat order

Joseph Newton

paper

Classifying quotients on Coxeter groups by isomorphism in Bruhat order

arXiv:2303.06619

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 $O$ for Kac-Moody algebras up to equivalence.

arXiv comment35 pages, 17 figures