Idempotents, traces, and dimensions in Hecke categories

Fuente: arXiv
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Hauptverfasser: Elias, Ben, Rogel, Liam, Tubbenhauer, Daniel
Format: Preprint
Veröffentlicht: 2025
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author Elias, Ben
Rogel, Liam
Tubbenhauer, Daniel
author_facet Elias, Ben
Rogel, Liam
Tubbenhauer, Daniel
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_10061
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Idempotents, traces, and dimensions in Hecke categories
Elias, Ben
Rogel, Liam
Tubbenhauer, Daniel
Representation Theory
Category Theory
Quantum Algebra
Primary 18M20, 20C08, Secondary 18M30, 18N25
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.
title Idempotents, traces, and dimensions in Hecke categories
topic Representation Theory
Category Theory
Quantum Algebra
Primary 18M20, 20C08, Secondary 18M30, 18N25
url https://arxiv.org/abs/2507.10061