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arXiv · 2506.05959

$q$-deformed Howe duality for orthosymplectic Lie superalgebras

Jeong Bae·Jae-Hoon Kwon
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Abstract

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 $\mf{g}=\mf{so}_{2n}$, $\mf{sp}_{2n}$.

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BibTeXRIS

Jeong Bae, Jae-Hoon Kwon. 2025-06-06. $q$-deformed Howe duality for orthosymplectic Lie superalgebras. https://arxiv.org/abs/2506.05959

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