# Tilting modules for classical Lie superalgebras

## TL;DR

This paper investigates tilting and projective-injective modules in the category O of classical Lie superalgebras, establishing duality results and classifying key modules with explicit combinatorial descriptions.

## Contribution

It introduces a version of Ringel duality for classical Lie superalgebras and classifies projective-injective modules in the full category O.

## Key findings

- Established Ringel duality for classical Lie superalgebras
- Classified projective-injective modules in category O
- Provided combinatorial descriptions of parabolic subalgebras

## Abstract

We study tilting and projective-injective modules in a parabolic BGG category $\mathcal O$ for an arbitrary classical Lie superalgebra. We establish a version of Ringel duality for this type of Lie superalgebras which allows to express the characters of tilting modules in terms of those of simple modules in that category. We also obtain a classification of projective-injective modules in the full BGG category $\mathcal O$ for all simple classical Lie superalgebras. We then classify and give an explicit combinatorial description of parabolic subalgebras of the periplectic Lie superalgebras and apply our results to study their tilting modules in more detail.