Matrix Capelli identities related to reflection equation algebra

Abstract

By using the notion of quantum double we introduce analogs of partial derivatives on a reflection equation algebra, associated with a Hecke symmetry of GLN 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 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 proved by A. Okounkov in [6].