论文标题
fock无穷大的空间和顶点操作员的字符
Fock Space of Level infinity and Characters of Vertex Operators
论文作者
论文摘要
我们提出了顶点操作员痕迹的扩展，并解释了对痕迹的表示理论解释。具体而言，我们考虑了带有无限许多Casimir操作员的顶点操作员的扭曲，并将其痕迹计算为角色公式。为此，我们定义了无限级别$ \ mathfrak {f}^{\ infty} $的fock空间。然后，我们证明了$ \ mathfrak {gl} _ {\ infty} $和$ \ mathfrak {a} _ {\ infty} = \ wideHat {\ m mathfrak {\ mathfrak {gl}} _ {\ mathfrak {\ mathfrak {gl}} _ {\ infty} $ deconffry a decomportty of a decomportty of a y matherty of a y Matty} $ {在具有$ \ mathfrak {gl} _ {\ infty} $和$ \ mathfrak {a} _ {\ iffty} $的不可减至的表示最高权重矢量中。 Fock空间的分解$ \ Mathfrak {f}^{\ infty} $中的最高权重表示提供了一种计算和解释扩展跟踪的方法。
We present an extension of the trace of a vertex operator and explain a representation-theoretic interpretation of the trace. Specifically, we consider a twist of the vertex operator with infinitely many Casimir operators and compute its trace as a character formula. To do this, we define the Fock space of infinite level $\mathfrak{F}^{\infty}$. Then, we prove a duality between $\mathfrak{gl}_{\infty}$ and $\mathfrak{a}_{\infty}=\widehat{\mathfrak{gl}}_{\infty}$ of Howe type, which provides a decomposition of $\mathfrak{F}^{\infty}$ into irreducible representations with joint highest weight vector for $\mathfrak{gl}_{\infty}$ and $\mathfrak{a}_{\infty}$. The decomposition of the Fock space $\mathfrak{F}^{\infty}$ into highest weight representations provides a method to calculate and interpret the extended trace.
