# The periplectic Brauer algebra II: decomposition multiplicities

## TL;DR

This paper calculates the decomposition multiplicities of modules over periplectic Brauer algebras in characteristic zero, using skew Young diagrams and connecting to Kazhdan-Lusztig theory for Lie superalgebras.

## Contribution

It introduces a combinatorial approach with skew Young diagrams to determine decomposition multiplicities and links these to Kazhdan-Lusztig multiplicities in the context of periplectic Lie superalgebras.

## Key findings

- Decomposition multiplicities are explicitly determined.
- A combinatorial framework using skew Young diagrams is developed.
- Connections to Kazhdan-Lusztig multiplicities are established.

## Abstract

We determine the Jordan-Holder decomposition multiplicities of projective and cell modules over periplectic Brauer algebras in characteristic zero. These are obtained by developing the combinatorics of certain skew Young diagrams. We also establish a useful relationship with the Kazhdan-Lusztig multiplicities of the periplectic Lie superalgebra.