Finite $W$-superalgebras for queer Lie superalgebras

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 $χ\in \ev\g^*$. 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.

The original submission was broken into two parts. This is the first part; the second part will posted later

References in corpus (1)

• Finite W-algebras

Cited by in corpus (4)

• Principal W-algebras for GL(m|n)
• Representations of Lie superalgebras in prime characteristic II: The queer series
• Dimensions of irreducible modules over W-algebras and Goldie ranks
• On Kostant's theorem for the Lie superalgebra Q(n)