This paper is to establish a natural connection of quantum affine algebras with quantum vertex algebras. Among the main results, we construct a family of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\hbar $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ħ</mi> </math></EquationSource> </InlineEquation>-adic quantum vertex algebras <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$V_L[[\hbar ]]^{\eta }$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>V</mi> <mi>L</mi> </msub> <msup> <mrow> <mo stretchy="false">[</mo> <mrow> <mo stretchy="false">[</mo> <mi>ħ</mi> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">]</mo> </mrow> <mi>η</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> as deformations of the lattice vertex algebras <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$V_L$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mi>L</mi> </msub> </math></EquationSource> </InlineEquation>, and establish a natural connection between twisted (and untwisted) quantum affine algebras of type A, D, or E and equivariant <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\phi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>-coordinated quasi modules for <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$V_L[[\hbar ]]^{\eta }$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>V</mi> <mi>L</mi> </msub> <msup> <mrow> <mo stretchy="false">[</mo> <mrow> <mo stretchy="false">[</mo> <mi>ħ</mi> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">]</mo> </mrow> <mi>η</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> with certain specialized <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\eta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>.

Twisted Quantum Affine Algebras and Equivariant $\phi $-Coordinated Modules for Quantum Vertex Algebras

期刊论文
发表日期：

2026年4月4日

查看全文

Naihuan Jing,
Fei Kong,
Haisheng Li,
Shaobin Tan

摘要

This paper is to establish a natural connection of quantum affine algebras with quantum vertex algebras. Among the main results, we construct a family of $\hbar $ $ħ$ -adic quantum vertex algebras $V_L[[\hbar ]]^{\eta }$ $V_{L} {[[ħ]]}^{η}$ as deformations of the lattice vertex algebras $V_L$ $V_{L}$ , and establish a natural connection between twisted (and untwisted) quantum affine algebras of type A, D, or E and equivariant $\phi $ $ϕ$ -coordinated quasi modules for $V_L[[\hbar ]]^{\eta }$ $V_{L} {[[ħ]]}^{η}$ with certain specialized $\eta $ $η$ .

Twisted Quantum Affine Algebras and Equivariant \(\phi \)-Coordinated Modules for Quantum Vertex Algebras

摘要