Jantzen filtration and strong linkage principle for modular Lie superalgebras

TL;DR

This paper develops a framework for understanding the structure of modules over basic classical Lie superalgebras in odd characteristic, introducing super Weyl groups, Jantzen filtrations, and a strong linkage principle.

Contribution

It introduces super Weyl groups and formulates Jantzen filtration and linkage principles for modular Lie superalgebras, extending classical representation theory tools.

Findings

Defined super Weyl groups and their properties.

Established a sum formula in Grothendieck groups.

Proved a strong linkage principle for modules.

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.