论文标题
量子仿射顶点代数与未twist的量子衰减代数相关
Quantum affine vertex algebras associated to untwisted quantum affinization algebras
论文作者
论文摘要
令$ \ mathcal u_ \ hbar（\ hat {\ mathfrak g}）$为不及格的量子量相关的量子量子，量子kac-moody algebra $ \ mathcal u_ \ hbar（{\ mathfrak g}）$。对于$ \ ell \ in \ mathbb c $，我们构造了一个$ \ hbar $ - addic量子顶点代数$ v _ {\ hat {\ mathfrak g}，\ hbar}（\ hbar}（\ ell，0）$ g}，\ hbar}（\ ell，0）$ - 模块和限制的$ \ mathcal u_ \ hbar（\ hat {\ mathfrak g}）$ - 级别$ \ ell $的模块。假设$ \ ell $是一个正整数。我们构建一个商$ \ hbar $ -adic量子顶点代数$ l _ {\ hat {\ mathfrak g}，\ hbar}，\ hbar}（\ ell，0）$ of $ v _ {\ hat {\ hat {\ mathfrak g} $ l _ {\ hat {\ mathfrak g}，\ hbar}（\ ell，0）$ - 模块和限制的集成$ \ mathcal u_ \ hbar（\ hat {\ hat {\ mathfrak g}）$ - 级别$ \ ell $的模块。进一步假设$ {\ mathfrak g} $是有限类型的。我们证明了$ l _ {\ hat {\ mathfrak g}，\ hbar}（\ ell，0）/\ hbar l _ {\ hat {\ hat {\ mathfrak g}，\ hbar}，\ hbar}（\ ell，0）$对简单的offine vertex algebra ungebra usgebra $ l _ { g}}（\ ell，0）$。
Let $\mathcal U_\hbar(\hat{\mathfrak g})$ be the untwisted quantum affinization of a symmetrizable quantum Kac-Moody algebra $\mathcal U_\hbar({\mathfrak g})$. For $\ell\in\mathbb C$, we construct an $\hbar$-adic quantum vertex algebra $V_{\hat{\mathfrak g},\hbar}(\ell,0)$, and establish a one-to-one correspondence between $ϕ$-coordinated $V_{\hat{\mathfrak g},\hbar}(\ell,0)$-modules and restricted $\mathcal U_\hbar(\hat{\mathfrak g})$-modules of level $\ell$. Suppose that $\ell$ is a positive integer. We construct a quotient $\hbar$-adic quantum vertex algebra $L_{\hat{\mathfrak g},\hbar}(\ell,0)$ of $V_{\hat{\mathfrak g},\hbar}(\ell,0)$, and establish a one-to-one correspondence between certain $ϕ$-coordinated $L_{\hat{\mathfrak g},\hbar}(\ell,0)$-modules and restricted integrable $\mathcal U_\hbar(\hat{\mathfrak g})$-modules of level $\ell$. Suppose further that ${\mathfrak g}$ is of finite type. We prove that $L_{\hat{\mathfrak g},\hbar}(\ell,0)/\hbar L_{\hat{\mathfrak g},\hbar}(\ell,0)$ is isomorphic to the simple affine vertex algebra $L_{\hat{\mathfrak g}}(\ell,0)$.
