Idempotents, traces, and dimensions in Hecke categories
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909688623267840 |
|---|---|
| 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 |