Symplectic tableaux and quantum symmetric pairs
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_ | 1866918017783300096 |
|---|---|
| author | Watanabe, Hideya |
| author_facet | Watanabe, Hideya |
| contents | We provide a new branching rule from the general linear group $GL_{2n}(\mathbb{C})$ to the symplectic group $Sp_{2n}(\mathbb{C})$ by establishing a simple algorithm which gives rise to a bijection from the set of semistandard tableaux of a fixed shape to a disjoint union of several copies of sets of symplectic tableaux of various shapes. The algorithm arises from representation theory of a quantum symmetric pair of type $A\mathrm{II}_{2n-1}$, which is a $q$-analogue of the classical symmetric pair $(\mathfrak{gl}_{2n}(\mathbb{C}), \mathfrak{sp}_{2n}(\mathbb{C}))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01718 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symplectic tableaux and quantum symmetric pairs Watanabe, Hideya Representation Theory Combinatorics Quantum Algebra 05E10, 17B10, 17B37 We provide a new branching rule from the general linear group $GL_{2n}(\mathbb{C})$ to the symplectic group $Sp_{2n}(\mathbb{C})$ by establishing a simple algorithm which gives rise to a bijection from the set of semistandard tableaux of a fixed shape to a disjoint union of several copies of sets of symplectic tableaux of various shapes. The algorithm arises from representation theory of a quantum symmetric pair of type $A\mathrm{II}_{2n-1}$, which is a $q$-analogue of the classical symmetric pair $(\mathfrak{gl}_{2n}(\mathbb{C}), \mathfrak{sp}_{2n}(\mathbb{C}))$. |
| title | Symplectic tableaux and quantum symmetric pairs |
| topic | Representation Theory Combinatorics Quantum Algebra 05E10, 17B10, 17B37 |
| url | https://arxiv.org/abs/2308.01718 |