The Regular Representation of the twisted queer $q$-Schur Superalgebra
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916738059206656 |
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| author | Li, Zhenhua |
| author_facet | Li, Zhenhua |
| contents | We study the representation theory of the quantum queer superalgebra ${U_{\lcase{v}}(\mathfrak{\lcase{q}}_{n})}$ and obtain some properties of the highest weight modules. Furthermore, based on the realization of ${U_{\lcase{v}}(\mathfrak{\lcase{q}}_{n})}$, we study the representation theory of the twisted queer $q$-Schur superalgebra ${\widetilde{\mathcal{Q}}_{\lcase{v}}(\lcase{n},\lcase{r})}$, and obtain the decomposition of its regular module as a direct sum of irreducible submodules, which also means ${\widetilde{\mathcal{Q}}_{\lcase{v}}(\lcase{n},\lcase{r})}$ is semisimple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10301 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Regular Representation of the twisted queer $q$-Schur Superalgebra Li, Zhenhua Quantum Algebra Representation Theory 17B37, 17A70, 20G42, 20C08 We study the representation theory of the quantum queer superalgebra ${U_{\lcase{v}}(\mathfrak{\lcase{q}}_{n})}$ and obtain some properties of the highest weight modules. Furthermore, based on the realization of ${U_{\lcase{v}}(\mathfrak{\lcase{q}}_{n})}$, we study the representation theory of the twisted queer $q$-Schur superalgebra ${\widetilde{\mathcal{Q}}_{\lcase{v}}(\lcase{n},\lcase{r})}$, and obtain the decomposition of its regular module as a direct sum of irreducible submodules, which also means ${\widetilde{\mathcal{Q}}_{\lcase{v}}(\lcase{n},\lcase{r})}$ is semisimple. |
| title | The Regular Representation of the twisted queer $q$-Schur Superalgebra |
| topic | Quantum Algebra Representation Theory 17B37, 17A70, 20G42, 20C08 |
| url | https://arxiv.org/abs/2505.10301 |