Extremal weight crystals over affine Lie algebras of infinite rank
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_ | 1866917879082909696 |
|---|---|
| author | Heo, Taehyeok |
| author_facet | Heo, Taehyeok |
| contents | We explain extremal weight crystals over affine Lie algebras of infinite rank using combinatorial models: a spinor model due to Kwon, and an infinite rank analogue of Kashiwara-Nakashima tableaux due to Lecouvey. In particular, we show that Lecouvey's tableau model is isomorphic to an extremal weight crystal of level zero. Using these combinatorial models, we explain an algebra structure of the Grothendieck ring for a category consisting of some extremal weight crystals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_05188 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extremal weight crystals over affine Lie algebras of infinite rank Heo, Taehyeok Representation Theory Quantum Algebra 17B37 (Primary) 17B10, 05E10, 17B65 (Secondary) We explain extremal weight crystals over affine Lie algebras of infinite rank using combinatorial models: a spinor model due to Kwon, and an infinite rank analogue of Kashiwara-Nakashima tableaux due to Lecouvey. In particular, we show that Lecouvey's tableau model is isomorphic to an extremal weight crystal of level zero. Using these combinatorial models, we explain an algebra structure of the Grothendieck ring for a category consisting of some extremal weight crystals. |
| title | Extremal weight crystals over affine Lie algebras of infinite rank |
| topic | Representation Theory Quantum Algebra 17B37 (Primary) 17B10, 05E10, 17B65 (Secondary) |
| url | https://arxiv.org/abs/2305.05188 |