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arXiv · 2507.10061

Idempotents, traces, and dimensions in Hecke categories

Ben Elias·Liam Rogel·Daniel Tubbenhauer
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Abstract

We explain how to compute idempotents that correspond to the indecomposable objects in the Hecke category. Closed formulas are provided for some common coefficients that appear in these idempotents. We also explain how to compute categorical dimensions in the asymptotic Hecke category. In many cases, we reduce this to a computation of a partial trace and give recursive formulas for some common partial traces. In the sequel, we apply this technology and perform additional (computer) calculations to complete the description of the asymptotic Hecke category for finite Coxeter groups in all but three cells.

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BibTeXRIS

Ben Elias, Liam Rogel, Daniel Tubbenhauer. 2025-07-14. Idempotents, traces, and dimensions in Hecke categories. https://arxiv.org/abs/2507.10061

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