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 $\mathfrak{pe}(3)$.

v2, 25 pages