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 $\mf{ g}=\mf{ so}_{ 2n}$, $\mf{ sp}_{ 2n}$.
Categories: math.RT