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Some remarks on realizations defining diagrammatic Hecke categories

2026/08/03 by Amit Hazi
Mathematics · #math.RT #msc:20C08 #msc:20G15 #msc:20F55

paper · pdf

16 pages, 5 figures

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

Every diagrammatic Hecke category is constructed from a realization, which generalizes the notion of a reflection representation of a Coxeter group. Common assumptions on realizations to ensure that the resulting categories are well behaved include Demazure surjectivity and the parabolic property (for anti-spherical quotients). We show that these assumptions are in fact unnecessary. We also give a non-inductive description of the rotational scalars for unbalanced realizations, as well as a simpler criterion to check for balancedness.

Citations