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arXiv · 2602.01130

A new new coproduct on quantum loop algebras

Andrei Neguţ
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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 use our construction to prove fundamental facts about representations of quantum loop algebras, such as the rationality of $R$-matrices, multiplicativity of $q$-characters, and polynomiality of theta series.

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Andrei Neguţ. 2026-02-01. A new new coproduct on quantum loop algebras. https://arxiv.org/abs/2602.01130

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