Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.05959 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915560747433984 |
|---|---|
| author | Bae, Jeong Kwon, Jae-Hoon |
| author_facet | Bae, Jeong Kwon, Jae-Hoon |
| contents | We give a $q$-analogue of Howe duality associated to a pair $(\mf{g},G)$, where $\mf{g}$ is an orthosymplectic Lie superalgebra and $G=O_\ell, Sp_{2\ell}$. We define explicitly {commuting actions} of a quantized enveloping algebra of $\mf{g}$ and the $\imath$quantum group of {type AI and AII} on a $q$-deformed supersymmetric space, and describe its semisimple decomposition whose classical limit recovers the $(\mf{g},G)$-duality. As special cases, we obtain $q$-analogues of $(\mf{g},G)$-dualities on symmetric and exterior algebras for $\mf{g}=\mf{so}_{2n}$, $\mf{sp}_{2n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $q$-deformed Howe duality for orthosymplectic Lie superalgebras Bae, Jeong Kwon, Jae-Hoon Representation Theory 17B37, 17B10 We give a $q$-analogue of Howe duality associated to a pair $(\mf{g},G)$, where $\mf{g}$ is an orthosymplectic Lie superalgebra and $G=O_\ell, Sp_{2\ell}$. We define explicitly {commuting actions} of a quantized enveloping algebra of $\mf{g}$ and the $\imath$quantum group of {type AI and AII} on a $q$-deformed supersymmetric space, and describe its semisimple decomposition whose classical limit recovers the $(\mf{g},G)$-duality. As special cases, we obtain $q$-analogues of $(\mf{g},G)$-dualities on symmetric and exterior algebras for $\mf{g}=\mf{so}_{2n}$, $\mf{sp}_{2n}$. |
| title | $q$-deformed Howe duality for orthosymplectic Lie superalgebras |
| topic | Representation Theory 17B37, 17B10 |
| url | https://arxiv.org/abs/2506.05959 |