On representations of quantum affine $\mathfrak{sl}_2$

TL;DR

This paper investigates the structure and interrelations of tensor products of 2D evaluation modules over the quantum affine algebra U_q(sl_2), focusing on homomorphisms and generic parameter values.

Contribution

It provides new insights into the homomorphisms between evaluation modules of U_q(sl_2) and their tensor product structures at generic q values.

Findings

Characterization of homomorphisms between evaluation modules

Analysis of tensor product decompositions at generic q

New results on module interrelations in quantum affine sl_2

Abstract

We study tensor products of two-dimensional evaluation $U_q\widehat{\mathfrak{sl}}_2$-modules at generic values of $q$, $U_q\widehat{\mathfrak{sl}}_2$ homomorphisms between them, and closely related subjects.