论文标题
量子均匀空间的Weyl代数
Weyl algebras for quantum homogeneous spaces
论文作者
论文摘要
我们提出了一个新的量子Weyl代数家族，其中多项式部分是对应于对称矩阵，偏斜对称矩阵以及给定大小的整个矩阵的均相空间上函数的量子类似物。该结构使用扭曲的张量产物及其变形，并结合量子对称对的不变性特性。这些量子Weyl代数接纳$ u_q（\ Mathfrak {gl} _n）$ - 模块代数结构与多项式部分上的标准关系兼容，具有通过矩阵很好地表达的关系，并且与量化量化的量子界界界的对称构造理论中产生的代数密切相关。
We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given size. The construction uses twisted tensor products and their deformations combined with invariance properties derived from quantum symmetric pairs. These quantum Weyl algebras admit $U_q(\mathfrak{gl}_N)$-module algebra structures compatible with standard ones on the polynomial part, have relations that are expressed nicely via matrices, and are closely related to an algebra arising in the theory of quantum bounded symmetric domains.
