Branching rules for level-zero extremal weight modules from $U_q(\widehat{\mathfrak{sl}}_{n+1})$ to $U_q(\widehat{\mathfrak{sl}}_n)$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911017791913984 |
|---|---|
| author | Nakaoka, Shutaro |
| author_facet | Nakaoka, Shutaro |
| contents | In this paper, we study the structure of a $U_q(\widehat{\mathfrak{sl}}_n)$-module $Ψ_{\varepsilon}^* V(λ)$, where $V(λ)$ is the extremal weight module of level-zero dominant weight $λ$ over the quantum affine algebra $U_q(\widehat{\mathfrak{sl}}_{n+1})$ and $Ψ_{\varepsilon}: U_q(\widehat{\mathfrak{sl}}_n) \to U_q(\widehat{\mathfrak{sl}}_{n+1})$ is an injective algebra homomorphism. We establish a direct sum decomposition $Ψ_{\varepsilon}^* V(λ) \cong M_{0,\varepsilon} \oplus \cdots \oplus M_{m,\varepsilon}$, where $M_{0,\varepsilon}$ and $M_{m,\varepsilon}$ are isomorphic to a tensor product of an extremal weight module over $U_q(\widehat{\mathfrak{sl}}_n)$ and a symmetric Laurent polynomial ring. Moreover, when $λ$ is a multiple of a level-zero fundamental weight, we show that $Ψ_{\varepsilon}^* V(λ)$ is isomorphic to a direct sum of extremal weight modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Branching rules for level-zero extremal weight modules from $U_q(\widehat{\mathfrak{sl}}_{n+1})$ to $U_q(\widehat{\mathfrak{sl}}_n)$ Nakaoka, Shutaro Representation Theory In this paper, we study the structure of a $U_q(\widehat{\mathfrak{sl}}_n)$-module $Ψ_{\varepsilon}^* V(λ)$, where $V(λ)$ is the extremal weight module of level-zero dominant weight $λ$ over the quantum affine algebra $U_q(\widehat{\mathfrak{sl}}_{n+1})$ and $Ψ_{\varepsilon}: U_q(\widehat{\mathfrak{sl}}_n) \to U_q(\widehat{\mathfrak{sl}}_{n+1})$ is an injective algebra homomorphism. We establish a direct sum decomposition $Ψ_{\varepsilon}^* V(λ) \cong M_{0,\varepsilon} \oplus \cdots \oplus M_{m,\varepsilon}$, where $M_{0,\varepsilon}$ and $M_{m,\varepsilon}$ are isomorphic to a tensor product of an extremal weight module over $U_q(\widehat{\mathfrak{sl}}_n)$ and a symmetric Laurent polynomial ring. Moreover, when $λ$ is a multiple of a level-zero fundamental weight, we show that $Ψ_{\varepsilon}^* V(λ)$ is isomorphic to a direct sum of extremal weight modules. |
| title | Branching rules for level-zero extremal weight modules from $U_q(\widehat{\mathfrak{sl}}_{n+1})$ to $U_q(\widehat{\mathfrak{sl}}_n)$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2501.11559 |