Jantzen filtration and strong linkage principle for modular Lie superalgebras

Abstract

In this paper, we introduce super Weyl groups, their distinguished elements and properties for basic classical Lie superalgebras. Then we formulate Jantzen filtration for baby Verma modules in graded restricted module categories of basic classical Lie superalgebras over an algebraically closed field of odd characteristic, and prove a sum formula in the corresponding Grothendieck groups. We finally obtain a strong linkage principle in such categories.

31pages

References in corpus (2)

• A new proof of the Mullineux conjecture
• Finite $W$-superalgebras and the dimensional lower bounds for the representations of basic Lie superalgebras