Finite W-superalgebras for queer Lie superalgebras

We initiate and develop the theory of finite W  -superalgebras WχWχ associated with the queer Lie superalgebra g=q(N)g=q(N) and a nilpotent linear functional χ∈g0¯⁎. 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 WχWχ-modules and a category of certain gg-modules.