On Finite W-Algebras for Lie Superalgebras in the Regular Case

Abstract

We study finite W-algebras corresponding to the regular nilpotent orbits for classical Lie superalgebras of Type I. In the case when the Lie superalgebra has defect 1 we give a complete description of the finite W-algebras. We also present some partial results for the case \(\mathfrak{g}\mathfrak{l}(n\vert n)\) and formulate a general conjecture about the structure of these algebras.