Non-archimedean Infinite Hecke Algebra
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915885305823232 |
|---|---|
| author | Weising, Milo Bechtloff |
| author_facet | Weising, Milo Bechtloff |
| contents | We study the representation theory of the infinite type A Hecke algebra over a non-archimedean field in the case where the parameter is a pseudo-uniformizer. Specifically, we consider a family of representations, called almost-symmetric, which satisfy additional topological and algebraic constraints. We construct a family of irreducible almost-symmetric representations indexed by integer partitions which arise as topological completions of specific direct limits of Hecke-Specht modules. Our main result is that every irreducible almost-symmetric representation contains one of these constructed irreducibles as a dense submodule. We give detailed analysis of these representations and construct functionals analogous to finite Hecke algebra traces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01835 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-archimedean Infinite Hecke Algebra Weising, Milo Bechtloff Representation Theory Combinatorics Operator Algebras We study the representation theory of the infinite type A Hecke algebra over a non-archimedean field in the case where the parameter is a pseudo-uniformizer. Specifically, we consider a family of representations, called almost-symmetric, which satisfy additional topological and algebraic constraints. We construct a family of irreducible almost-symmetric representations indexed by integer partitions which arise as topological completions of specific direct limits of Hecke-Specht modules. Our main result is that every irreducible almost-symmetric representation contains one of these constructed irreducibles as a dense submodule. We give detailed analysis of these representations and construct functionals analogous to finite Hecke algebra traces. |
| title | Non-archimedean Infinite Hecke Algebra |
| topic | Representation Theory Combinatorics Operator Algebras |
| url | https://arxiv.org/abs/2512.01835 |