论文标题
延长的仿期为代数，顶点代数和还原组
Extended affine Lie algebras, vertex algebras, and reductive groups
论文作者
论文摘要
在本文中，我们探讨了扩展的仿射词的自然连接，代数$ \ wideHat {sl_n}（\ Mathbb {c} _q）$与$ \ mathbb {c} _q} _q = \ \ m mathbb {c} 2-torus，简单的仿射顶点algebra $ l _ {\ wideHat {sl _ {\ infty}}}}}}（\ ell，0）$带有$ \ ell $ a正整数，levi子组$ g $ g of $ gl_ \ gl_ \ ell（\ ell（\ mathbb {c c} c}）$。首先，我们在可集成限制的$ \ wideHat {sl_n}（\ Mathbb {c} _q）$ - 等级$ \ ell $的模块与Equivariant Quasi Quasi Quasi $ l _ {\ wideHat {\ sl _ {sl _ {$ nod）之间给出了一个规范的同构。其次，我们将不可理用的$ \ mathbb {n} $ - 分级epivariant quasi $ l _ {\ wideHat {sl _ {\ infty}}}（\ ell，0）$ - 模块。第三，我们建立了不可约合$ \ mathbb {n} $ - 分级的equivariant quasi $ l _ {\ wideHat {sl _ {\ infty}}}}}（\ ell，0）$ - 模块 - 模块和不可修复的常规$ g $ -Modules在某些fermerionic fock spaces上。第四，我们获得了每个不可约的$ \ mathbb {n} $ - 分级equivariant quasi $ l _ {\ wideHat {sl _ {\ infty}}}}}（\ ell，0）$ - $ - 模块。第五，我们完全确定以下分支：1 $ l _ {\ wideHat {sl _ {\ infty}}}}}}}}（\ ell，0）\ otimes l _ {\ wideHat { $ l _ {\ wideHat {sl _ {\ infty}}}}}}（\ ell+\ ell'，0）$用于准模块。 2从$ \ wideHat {sl_n}（\ mathbb {c} _q）$分支到其levi subalgebras。 3从$ \ wideHat {sl_n}（\ mathbb {c} _q）$到其subalgebras $ \ wideHat {sl_n}（\ Mathbb {c} _q [t_0^{
In this paper, we explore natural connections among the representations of the extended affine Lie algebra $\widehat{sl_N}(\mathbb{C}_q)$ with $\mathbb{C}_q=\mathbb{C}_q[t_0^{\pm1},t_1^{\pm1}]$ an irrational quantum 2-torus, the simple affine vertex algebra $L_{\widehat{sl_{\infty}}}(\ell,0)$ with $\ell$ a positive integer, and Levi subgroups $G$ of $GL_\ell(\mathbb{C})$. First, we give a canonical isomorphism between the category of integrable restricted $\widehat{sl_N}(\mathbb{C}_q)$-modules of level $\ell$ and that of equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$-modules. Second, we classify irreducible $\mathbb{N}$-graded equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$-modules. Third, we establish a duality between irreducible $\mathbb{N}$-graded equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$-modules and irreducible regular $G$-modules on certain fermionic Fock spaces. Fourth, we obtain an explicit realization of every irreducible $\mathbb{N}$-graded equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$-module. Fifth, we completely determine the following branchings: 1 The branching from $L_{\widehat{sl_{\infty}}}(\ell,0)\otimes L_{\widehat{sl_{\infty}}}(\ell',0)$ to $L_{\widehat{sl_{\infty}}}(\ell+\ell',0)$ for quasi modules. 2 The branching from $\widehat{sl_N}(\mathbb{C}_q)$ to its Levi subalgebras. 3 The branching from $\widehat{sl_N}(\mathbb{C}_q)$ to its subalgebras $\widehat{sl_N}(\mathbb{C}_q[t_0^{\pm M_0},t_1^{\pm M_1}])$.
