A new new coproduct on quantum loop algebras

TL;DR

This paper introduces a new coproduct for quantum loop algebras that extends the Drinfeld-Jimbo coproduct, impacting their representation theory and tensor product structures.

Contribution

It defines a novel coproduct on quantum loop algebras, generalizing existing structures and exploring implications for modules and R-matrices.

Findings

Coproduct coincides with Drinfeld-Jimbo in specific cases

Impacts tensor product structures of modules

Provides new tools for representation theory

Abstract

Quantum loop algebras generalize $U_q(\widehat{\mathfrak{g}})$ for simple Lie algebras $\mathfrak{g}$, and they include examples such as quantum affinizations of Kac-Moody Lie algebras, K-theoretic Hall algebras of quivers, and BPS algebras for toric Calabi-Yau threefolds. In the present paper, we define a coproduct on general quantum loop algebras, which coincides with the Drinfeld-Jimbo coproduct in the particular case of $U_q(\widehat{\mathfrak{g}})$ . We investigate the consequences of our construction for the representation theory of quantum loop algebras, particularly for tensor products of modules and R-matrices.