Branching rules for quantum toroidal gl(n)

TL;DR

This paper constructs a subalgebra analog within quantum toroidal algebras and investigates how different representations behave when restricted to this subalgebra.

Contribution

It introduces a new subalgebra in quantum toroidal algebras and analyzes the restriction of representations, expanding understanding of their structure.

Findings

Construction of the subalgebra in quantum toroidal algebras.

Analysis of representation restrictions to the subalgebra.

Insights into the structure of quantum toroidal algebras.

Abstract

We construct an analog of the subalgebra $Ugl(n)\otimes Ugl(m)$ of $Ugl(m+n)$ in the setting of quantum toroidal algebras and study the restrictions of various representations to this subalgebra.