The Garnir Relations for Weyl Groups

TL;DR

This paper extends the Garnir relations, originally significant in symmetric group representation theory, to the broader context of Weyl groups, potentially broadening their applicability.

Contribution

It introduces a possible extension of Garnir relations from symmetric groups to general Weyl groups, expanding their theoretical framework.

Findings

Proposed a generalized form of Garnir relations for Weyl groups

Established foundational properties for the extended relations

Potential implications for representation theory of Weyl groups

Abstract

The so-called Garnir relations are very important in the representation theory of the symmetric groups. In this paper, we give a possible extension of Garnir relations for Weyl groups in general.