Symplectic cacti, virtualization and Berenstein-Kirillov groups
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909738602594304 |
|---|---|
| author | Azenhas, Olga Feller, Mojdeh Tarighat Torres, Jacinta |
| author_facet | Azenhas, Olga Feller, Mojdeh Tarighat Torres, Jacinta |
| contents | We explicitly realize an internal action of the symplectic cactus group, recently defined by Halacheva for any complex, reductive, finite-dimensional Lie algebra, on crystals of Kashiwara-Nakashima tableaux. Our methods include a symplectic version of jeu de taquin due to Sheats and Lecouvey, symplectic reversal, and virtualization due to Baker. As an application, we define and study a symplectic version of the Berenstein-Kirillov group and show that it is a quotient of the symplectic cactus group. In addition two relations for symplectic Berenstein-Kirillov group are given that do not follow from the defining relations of the symplectic cactus group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_08446 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Symplectic cacti, virtualization and Berenstein-Kirillov groups Azenhas, Olga Feller, Mojdeh Tarighat Torres, Jacinta Representation Theory Combinatorics We explicitly realize an internal action of the symplectic cactus group, recently defined by Halacheva for any complex, reductive, finite-dimensional Lie algebra, on crystals of Kashiwara-Nakashima tableaux. Our methods include a symplectic version of jeu de taquin due to Sheats and Lecouvey, symplectic reversal, and virtualization due to Baker. As an application, we define and study a symplectic version of the Berenstein-Kirillov group and show that it is a quotient of the symplectic cactus group. In addition two relations for symplectic Berenstein-Kirillov group are given that do not follow from the defining relations of the symplectic cactus group. |
| title | Symplectic cacti, virtualization and Berenstein-Kirillov groups |
| topic | Representation Theory Combinatorics |
| url | https://arxiv.org/abs/2207.08446 |