Classifying quotients on Coxeter groups by isomorphism in Bruhat order

2023/03/12 by Newton, Joseph
#06A07 #17B67 #20F55 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/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 \mathcal O for Kac-Moody algebras up to equivalence.

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