Quantum loop algebras and l-root operators

TL;DR

This paper introduces an algebra A related to quantum loop algebras that acts on a specific category of finite-dimensional representations, providing a new framework for understanding their structure.

Contribution

It constructs an algebra A with operators of definite l-weight and establishes a homomorphism from Uq(Lg) to A, linking their representation theories.

Findings

Defined algebra A with l-weight specific operators

Established a homomorphism from Uq(Lg) to A

Showed all representations in C_P are pull-backs from A

Abstract

Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data (g,q,P), we define an algebra A whose raising/lowering operators are constructed to act with definite l-weight (unlike those of Uq(Lg) itself). It is shown that there is a homomorphism Uq(Lg) -> A such that every representation V in C_P is the pull-back of a representation of A.