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arXiv · 2212.01895

Twisted quantum affine algebras and equivariant $ϕ$-coordinated modules for quantum vertex algebras

Naihuan Jing·Fei Kong·Haisheng Li·Shaobin Tan
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Abstract

This paper is about establishing a natural connection of quantum affine algebras with quantum vertex algebras. Among the main results, we establish $\hbar$-adic versions of the smash product construction of quantum vertex algebras and their $ϕ$-coordinated quasi modules, which were obtained before in a sequel, we construct a family of $\hbar$-adic quantum vertex algebras $V_L[[\hbar]]^η$ as deformations of the lattice vertex algebras $V_L$, and establish a natural connection between twisted quantum affine algebras of type $A, D, E$ and equivariant $ϕ$-coordinated quasi modules for the $\hbar$-adic quantum vertex algebras $V_L[[\hbar]]^η$ with certain specialized $η$.

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Naihuan Jing, Fei Kong, Haisheng Li, Shaobin Tan. 2022-12-04. Twisted quantum affine algebras and equivariant $ϕ$-coordinated modules for quantum vertex algebras. https://doi.org/10.1007/s00220-026-05621-5

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