2026/08/03 by Amit Hazi
Mathematics · #math.RT #msc:20C08 #msc:20G15 #msc:20F55
16 pages, 5 figures
arxiv created 2026/08/03 · arxiv updated 2026/08/04
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.