Parabolic category ${\mathcal{O}}^{\mathfrak{p}}$ for periplectic Lie superalgebras $\mathfrak{pe}(n)$

Abstract

We provide a linkage principle in an arbitrary parabolic category ${\mathcal{O}}^{\mathfrak{p}}$ for the periplectic Lie superalgebras $\mathfrak{pe}(n)$. As an application, we classify indecomposable blocks in ${\mathcal{O}}^{\mathfrak{p}}$. We classify indecomposable tilting modules in ${\mathcal{O}}^{\mathfrak{p}}$ whose characters are controlled by the Kazhdan-Lusztig polynomials of type $\mathbf{A}$ Lie algebras. We establish the complete list of characters of indecomposable tilting modules in ${\mathcal{O}}^{\mathfrak{p}}$ for $\mathfrak{pe}(3)$.

arXiv commentv2, 25 pages

References in corpus (9)

• A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
• Tensor product categorifications and the super Kazhdan-Lusztig conjecture
• On representations of the Lie superalgebra p(n)
• Equivalence of blocks for the general linear Lie superalgebra
• Semi-infinite highest weight categories
• Duflo-Serganova functor and superdimension formula for the periplectic Lie superalgebra
• Character formulae in category $\mathcal{O}$ for exceptional Lie superalgebras $D(2|1;\zeta )$
• The affine VW supercategory
• Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras

Cited by in corpus (1)

• Whittaker modules for classical Lie superalgebras