q-deformed Howe duality for orthosymplectic Lie superalgebras
Abstract
We give a q-analogue of Howe duality associated to a pair (g,G), where g is an orthosymplectic Lie superalgebra and G=O, Sp2. We define explicitly commuting actions of a quantized enveloping algebra of g and the group of type AI and AII on a q-deformed supersymmetric space, and describe its semisimple decomposition whose classical limit recovers the (g,G)-duality. As special cases, we obtain q-analogues of (g,G)-dualities on symmetric and exterior algebras for g=so2n, sp2n.
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