量子仿射w -代数的模不变性

IF 2.2 1区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL
Victor G. Kac, Minoru Wakimoto
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引用次数: 0

摘要

我们找到了以下w -代数的规范化字符的模变换:(a) \(W_k^{min}(\mathfrak {g}), \text {where } \mathfrak {g}=D_n (n\ge 4), \text {or } E_6, E_7, E_8,\)和k分别是负整数\(\ge -2\),或\(\ge -\frac{h^\vee }{6}-1\);(b) \(\hat{\mathfrak {g}}\) -模\(L(k \Lambda _0)\)的量子哈密顿化约,其中\(\mathfrak {g}\)是一个简单李代数,f是它的非零幂零元,k是一个以\(u>\theta (x)\)为分母的主容许阶,其中2x是f的Dynkin特性,\(\theta \)是\(\mathfrak {g}\)的最高根。证明了这些顶点代数是模不变的。如果一个共形顶点代数V的性质\(tr_V q^{L_0-c/24}\)收敛于一个同余子群上复半平面上的全纯模函数,则称其为模不变量。我们为他们的性格找到了明确的公式。V的模不变性是重要的,因为,在推测上,它意味着V是简单的,而V是有理的,只要它是lisse。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On Modular Invariance of Quantum Affine W-Algebras

We find modular transformations of normalized characters for the following W-algebras: (a) \(W_k^{min}(\mathfrak {g}), \text {where } \mathfrak {g}=D_n (n\ge 4), \text {or } E_6, E_7, E_8,\) and k is a negative integer \(\ge -2\), or \(\ge -\frac{h^\vee }{6}-1\), respectively; (b) quantum Hamiltonian reduction of the \(\hat{\mathfrak {g}}\)-module \(L(k \Lambda _0)\), where \(\mathfrak {g}\) is a simple Lie algebra, f is its non-zero nilpotent element, and k is a principal admissible level with the denominator \(u>\theta (x)\), where 2x is the Dynkin characteristic of f, and \(\theta \) is the highest root of \(\mathfrak {g}\). We prove that these vertex algebras are modular invariant. A conformal vertex algebra V is called modular invariant if its character \(tr_V q^{L_0-c/24}\) converges to a holomorphic modular function in the complex upper half-plane on a congruence subgroup. We find explicit formulas for their characters. Modular invariance of V is important since, in particular, conjecturally it implies that V is simple, and that V is rational, provided that it is lisse.

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来源期刊
Communications in Mathematical Physics
Communications in Mathematical Physics 物理-物理:数学物理
CiteScore
4.70
自引率
8.30%
发文量
226
审稿时长
3-6 weeks
期刊介绍: The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
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