Inflations among quantum Grothendieck rings of type A
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914122596089856 |
|---|---|
| author | Fujita, Ryo |
| author_facet | Fujita, Ryo |
| contents | We introduce a collection of injective homomorphisms among the quantum Grothendieck rings of finite-dimensional modules over the quantum loop algebras of type $\mathrm{A}$. In the classical limit, it specializes to the inflation among the usual Grothendieck rings studied by Brito-Chari [J. Reine Angew. Math. 804, 2023]. We show that our homomorphisms respect the canonical bases formed by the simple $(q,t)$-characters, which in particular verifies a conjecture of Brito-Chari in loc. cit. We also discuss a categorification of our homomorphisms using the quiver Hecke algebras of type $\mathrm{A}_\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inflations among quantum Grothendieck rings of type A Fujita, Ryo Quantum Algebra 17B37, 81R50 We introduce a collection of injective homomorphisms among the quantum Grothendieck rings of finite-dimensional modules over the quantum loop algebras of type $\mathrm{A}$. In the classical limit, it specializes to the inflation among the usual Grothendieck rings studied by Brito-Chari [J. Reine Angew. Math. 804, 2023]. We show that our homomorphisms respect the canonical bases formed by the simple $(q,t)$-characters, which in particular verifies a conjecture of Brito-Chari in loc. cit. We also discuss a categorification of our homomorphisms using the quiver Hecke algebras of type $\mathrm{A}_\infty$. |
| title | Inflations among quantum Grothendieck rings of type A |
| topic | Quantum Algebra 17B37, 81R50 |
| url | https://arxiv.org/abs/2412.11881 |