A generalization of Kac polynomials and tensor product of representations of $GL_n(\mathbb{F}_q)$
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909370998063104 |
|---|---|
| author | Scognamiglio, Tommaso |
| author_facet | Scognamiglio, Tommaso |
| contents | We study the multiplicities of semisimple split characters in tensor product of semisimple split characters of $GL_n(\mathbb{F}_q)$. We prove that these multiplicities are polynomial in q with non-negative integer coefficients and we obtain a criterion for their non-vanishing. We give moreover an interpretation of these polynomials in terms of the counting of the representations of star-shaped quivers, generalizing a previous result of Hausel, Letellier and Rodriguez-Villegas, who linked multiplicities for generic $k$-tuples of semisimple split characters and Kac polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_08950 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A generalization of Kac polynomials and tensor product of representations of $GL_n(\mathbb{F}_q)$ Scognamiglio, Tommaso Representation Theory We study the multiplicities of semisimple split characters in tensor product of semisimple split characters of $GL_n(\mathbb{F}_q)$. We prove that these multiplicities are polynomial in q with non-negative integer coefficients and we obtain a criterion for their non-vanishing. We give moreover an interpretation of these polynomials in terms of the counting of the representations of star-shaped quivers, generalizing a previous result of Hausel, Letellier and Rodriguez-Villegas, who linked multiplicities for generic $k$-tuples of semisimple split characters and Kac polynomials. |
| title | A generalization of Kac polynomials and tensor product of representations of $GL_n(\mathbb{F}_q)$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2306.08950 |