Graphic Interpretation of the Structure Constants of the Schur Algebra

TL;DR

This paper introduces a new graphical interpretation of the basis of the Schur algebra and uses it to describe its structure constants, building on previous graph-theoretic approaches.

Contribution

It provides a novel graphical perspective on Schur algebra basis and structure constants, offering an alternative to existing descriptions.

Findings

New graphical interpretation of Schur algebra basis

Equivalent description of structure constants using graphs

Simplifies understanding of Schur algebra structure

Abstract

Issai Schur, in his doctoral thesis (1901) introduced the Schur algebra to study the polynomial representation theory of the general linear group. He described a basis of this algebra and structure constants. Later, Miguel Mendez (2001) gave a graph-theoretic description of Schur's basis and computed the structure constants. In this presentation, we will give a new graphic interpretation of the basis of Schur algebra and use it to give a description of the structure constants which is equivalent to the one given by Mendez.