论文标题
$ r $ $矩阵，用于$ a $ $ a $的通用量子组
$R$ matrix for generalized quantum group of type $A$
论文作者
论文摘要
类型$ a $的广义量子组$ \ MATHCAL {U}（ε）$是与一般线性lie lie superalgebra $ \ mathfrak {gl} _ {m | n} $相关的量子组的仿真类似物。我们证明，在张量的产品上存在一个唯一的$ r $矩阵，该张量产物的基本类型表示形式的$ \ Mathcal {u}（ε）$用于任意参数序列$ε$，对应于非偶联的borel borel borel subalgebra $ \ mathfrak {gl} _ {gl} _ {m | n} $。我们对其光谱分解进行了明确的描述，然后作为应用程序，构建了一个有限维度不可约的$ \ Mathcal {u}（U}（ε）$ - 具有同构的模块，这些模块属于Kirillov-reshetikhin模块，用于kirillov-reshetikhin模块$ a_ {n-1}^{（1）} $。
The generalized quantum group $\mathcal{U}(ε)$ of type $A$ is an affine analogue of quantum group associated to a general linear Lie superalgebra $\mathfrak{gl}_{M|N}$. We prove that there exists a unique $R$ matrix on tensor product of fundamental type representations of $\mathcal{U}(ε)$ for arbitrary parameter sequence $ε$ corresponding to a non-conjugate Borel subalgebra of $\mathfrak{gl}_{M|N}$. We give an explicit description of its spectral decomposition, and then as an application, construct a family of finite-dimensional irreducible $\mathcal{U}(ε)$-modules which have subspaces isomorphic to the Kirillov-Reshetikhin modules of usual affine type $A_{M-1}^{(1)}$ or $A_{N-1}^{(1)}$.
