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arXiv · 2608.02187

Some remarks on realizations defining diagrammatic Hecke categories

Amit Hazi
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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.

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Amit Hazi. 2026-08-03. Some remarks on realizations defining diagrammatic Hecke categories. https://arxiv.org/abs/2608.02187

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