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.

arXiv comment29 pages, version 2, minor revision. Comments welcome

References in corpus (18)

• A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
• Whittaker modules for the affine Lie algebra $A_1^{(1)}$
• Whittaker Modules for the twisted Heisenberg-Virasoro Algebra
• Super duality and irreducible characters of ortho-symplectic Lie superalgebras
• On representations of the Lie superalgebra p(n)
• Equivalence of blocks for the general linear Lie superalgebra
• Semi-infinite highest weight categories
• Generalized oscillator representations of the twisted Heisenberg-Virasoro algebra
• Tilting modules for classical Lie superalgebras
• Classification of irreducible Harish-Chandra modules over the loop-Virasoro algebra
• Koszul duality for semidirect products and generalized Takiff algebras
• Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules
• Projective and Whittaker functors on category $\mathcal{O}$
• Gorenstein homological algebra for rngs and Lie superalgebras
• The primitive spectrum and category O for the periplectic Lie superalgebra
• Parabolic category ${\mathcal{O}}^{\mathfrak{p}}$ for periplectic Lie superalgebras $\mathfrak{pe}(n)$
• The Heisenberg-Virasoro Lie conformal superalgebra
• Blocks and characters of $G(3)$-modules of non-integral weights

Cited by in corpus (5)

• Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras
• Whittaker category for the Lie algebra of polynomial vector fields
• Whittaker modules for a subalgebra of N=2 superconformal algebra
• Annihilator ideals and blocks of Whittaker modules over quasireductive Lie superalgebras
• On finite dimensional representations of finite W-superalgebras