Fock Space Representation of the Circle Quantum Group
Fock Space Representation of the Circle Quantum Group
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DOI：
10.1093/imrn/rnz268
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发表时间：
2019-03
影响因子：
1
通讯作者：
Francesco Sala;O. Schiffmann
中科院分区：
文献类型：
--
作者：
Francesco Sala;O. Schiffmann
在文[12]中，我们定义了量子群$\mathbf{U}_{\upsilon}(\mathfrak{sl}(\mathbb{R}))$和$\mathbf{U}_{\upsilon}(\mathfrak{sl}(S^1))$，它们可以解释为有限的分别仿射类型的Kac-Moody李代数的量子群的连续统推广。本文定义量子群$\mathbf{U}_{\upsilon}(\mathfrak{sl}(\mathbb{R}))$的Fock空间表示$\mathcal{F}_{\mathbb{R}}$为实金字塔生成的向量空间(划分概念的连续推广)。此外，利用Hayashi-Misra-Miwa的“折叠过程”的变体，我们定义了$\mathbf{U}_{\upsilon}(\mathfrak{sl}(S^1))$对$\mathcal{F}_{\mathbb{R}}$的作用。
In [12] we have defined quantum groups $\mathbf{U}_{\upsilon }(\mathfrak{sl}(\mathbb{R}))$ and $\mathbf{U}_{\upsilon }(\mathfrak{sl}(S^1))$, which can be interpreted as continuum generalizations of the quantum groups of the Kac–Moody Lie algebras of finite, respectively affine type $A$. In the present paper, we define the Fock space representation $\mathcal{F}_{\mathbb{R}}$ of the quantum group $\mathbf{U}_{\upsilon }(\mathfrak{sl}(\mathbb{R}))$ as the vector space generated by real pyramids (a continuum generalization of the notion of partition). In addition, by using a variant version of the “folding procedure” of Hayashi–Misra–Miwa, we define an action of $\mathbf{U}_{\upsilon }(\mathfrak{sl}(S^1))$ on $\mathcal{F}_{\mathbb{R}}$.