Proves Hernandez conjecture on q-character equality for twisted and untwisted quantum affine modules via folding shuffle algebras and generalizes to twisted quantum toroidal algebras.
A new new coproduct on quantum loop algebras
2 Pith papers cite this work. Polarity classification is still indexing.
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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.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Derives conjugation formulas for unitriangular R-matrices of quantum affine algebras and Yangians using T-series of Frenkel-Hernandez and prior Theta series.
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Folding shuffle algebras and twisted $q$-characters
Proves Hernandez conjecture on q-character equality for twisted and untwisted quantum affine modules via folding shuffle algebras and generalizes to twisted quantum toroidal algebras.
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Unitriangular R-matrices of quantum affine algebras and Yangians via Theta series
Derives conjugation formulas for unitriangular R-matrices of quantum affine algebras and Yangians using T-series of Frenkel-Hernandez and prior Theta series.