Growth Problems for Representations of Finite Monoids
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918426823360512 |
|---|---|
| author | He, David Tubbenhauer, Daniel |
| author_facet | He, David Tubbenhauer, Daniel |
| contents | We give a conjecture for the asymptotic growth rate of the number of indecomposable summands in the tensor powers of representations of finite monoids, expressing it in terms of the (Brauer) character table of the monoid's group of units. We prove it under an additional hypothesis. We also give (exact and asymptotic) formulas for the growth rate of the length of the tensor powers when working over a good characteristic. As examples, we compute the growth rates for the full transformation monoid, the symmetric inverse monoid, and the monoid of 2 by 2 matrices. We also provide code used for our calculation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Growth Problems for Representations of Finite Monoids He, David Tubbenhauer, Daniel Representation Theory Category Theory Primary: Primary: 11N45, 18M05, Secondary: 20M20, 20M30 We give a conjecture for the asymptotic growth rate of the number of indecomposable summands in the tensor powers of representations of finite monoids, expressing it in terms of the (Brauer) character table of the monoid's group of units. We prove it under an additional hypothesis. We also give (exact and asymptotic) formulas for the growth rate of the length of the tensor powers when working over a good characteristic. As examples, we compute the growth rates for the full transformation monoid, the symmetric inverse monoid, and the monoid of 2 by 2 matrices. We also provide code used for our calculation. |
| title | Growth Problems for Representations of Finite Monoids |
| topic | Representation Theory Category Theory Primary: Primary: 11N45, 18M05, Secondary: 20M20, 20M30 |
| url | https://arxiv.org/abs/2502.02849 |