Structure constants of diagonal reduction algebras of gl type

TL;DR

This paper characterizes the structure constants of diagonal reduction algebras of gl type using generators and relations, linking their representation theory to tensor product decompositions of gl modules.

Contribution

It provides a detailed description of the algebra's structure constants and relations, advancing understanding of diagonal reduction algebras of gl type.

Findings

Explicit generators and relations for the algebra

Connection established between algebra structure and tensor product decompositions

Foundation laid for further representation-theoretic analysis

Abstract

We describe, in terms of generators and relations, the reduction algebra, related to the diagonal embedding of the Lie algebra $\gl_n$ into $\gl_n\oplus\gl_n$. Its representation theory is related to the theory of decompositions of tensor products of $\gl_n$-modules.