论文标题
与反射方程相关的矩阵Capelli身份
Matrix Capelli identities related to Reflection Equation algebra
论文作者
论文摘要
通过使用量子双重的概念，我们在反射方程代数上引入了部分衍生物的类似物，该代数与GL（N）类型的Hecke对称性有关。我们构造矩阵L = MD，其中m是反射方程代数的生成矩阵，D是由量子部分衍生物组成的矩阵，并证明矩阵m，d和l满足矩阵身份，称为矩阵capelli capelli。应用量子迹线后，它成为标量关系，这是经典Capelli身份的深远概括。另外，我们得到了A.Okounkov定义的一些更高的Capelli身份的概括。
By using the notion of a quantum double we introduce analogs of partial derivatives on a Reflection Equation algebra, associated with a Hecke symmetry of GL(N) type. We construct the matrix L=MD, where M is the generating matrix of the Reflection Equation algebra and D is the matrix composed of the quantum partial derivatives and prove that the matrices M, D and L satisfy a matrix identity, called the matrix Capelli one. Upon applying the quantum trace, it becomes a scalar relation, which is a far-reaching generalization of the classical Capelli identity. Also, we get a generalization of the some higher Capelli identities defined by A.Okounkov.
