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Finite $W$-superalgebras for queer Lie superalgebras (1012.2326v2)

Published 10 Dec 2010 in math.RT

Abstract: We initiate and develop the theory of finite $W$-superalgebras $\mathcal{W}\chi$ associated to the queer Lie superalgebra $\g=\q(N)$ and a nilpotent linear functional $\chi \in \ev\g*$. We show that the definition of the $W$-superalgebra is independent of various choices. We also establish a Skryabin type equivalence between the category of $\mathcal{W}\chi$-modules and a category of certain $\g$-modules.

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