Brauer Algebras of multiply laced Weyl type

TL;DR

This paper defines Brauer algebras for Weyl types, focusing on non-simply laced types like G2, and establishes foundational propositions for these algebras.

Contribution

It introduces the concept of Brauer algebras for Weyl types and proves key results for type G2, advancing the understanding of non-simply laced cases.

Findings

Defined Brauer algebras of Weyl types

Proved propositions for these algebras

Established results for type G2

Abstract

In this paper, we will define the Brauer algebras of Weyl types, and describe some propositions of these algebras. Especially, we prove the result of type $G_2$ to accomplish our project of Brauer algebras of non-simply laced types.