Whittaker Modules for Classical Lie Superalgebras

Abstract

We classify simple Whittaker modules for classical Lie superalgebras in terms of their parabolic decompositions. We establish a type of Miličić–Soergel equivalence of a category of Whittaker modules and a category of Harish–Chandra bimodules. For classical Lie superalgebras of type I, we reduce the problem of composition factors of standard Whittaker modules to that of Verma modules in their BGG categories $${\mathcal {O}}$$ . As a consequence, the composition series of standard Whittaker modules over the general linear Lie superalgebras $$\mathfrak {gl}(m|n)$$ and the ortho-symplectic Lie superalgebras $$\mathfrak {osp}(2|2n)$$ can be computed via the Kazhdan–Lusztig combinatorics.