The blocks of the Brauer algebra in characteristic p

TL;DR

This paper provides a comprehensive description of the limiting blocks of Brauer algebras over fields of positive characteristic and establishes the existence of specific homomorphisms between cell modules.

Contribution

It offers a complete characterization of limiting blocks in Brauer algebras in positive characteristic and introduces new homomorphisms between cell modules.

Findings

Complete description of limiting blocks over any field of positive characteristic

Proof of existence of homomorphisms between cell modules

Advancement in understanding the structure of Brauer algebras

Abstract

Brauer algebras form a tower of cellular algebras. There is a well-defined notion of limiting blocks for these algebras. In this paper we give a complete description of these limiting blocks over any field of positive characteristic. We also prove the existence of a class of homomorphisms between cell modules.