Data

• Title: Idempotents, traces, and dimensions in Hecke categories
• Authors: Ben Elias, Liam Rogel and Daniel Tubbenhauer
• Status: preprint. Last update: Wed, 5 Feb 2025 03:03:57 UTC
• Code and (possibly empty) Erratum: Click
• ArXiv link: http://arxiv.org/abs/2503.00685

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.

A few extra words

This paper is a user's guide about Idempotents in Hecke categories, with fancy pictures like: