Generalized Harish-Chandra morphism on Reflection Equation algebras

TL;DR

This paper extends the Harish-Chandra morphism to Reflection Equation algebras, enabling the construction of quantum analogs of weight systems and enriching the algebraic framework for quantum symmetries.

Contribution

It generalizes the Harish-Chandra morphism to Reflection Equation algebras associated with Hecke symmetries, introducing quantum weight systems.

Findings

Defined eigenvalues for Reflection Equation algebra matrices

Constructed quantum analogs of weight systems

Extended the Harish-Chandra morphism to new algebraic structures

Abstract

We consider the so-called generalized Harish-Chandra morphism, taking the center of the enveloping algebra U(gl(N)) to the commutative algebra generated by eigenvalues of the generating matrix of this algebra, and generalize this construction to Reflection Equation algebras. To this end we introduce the eigenvalues of the generating matrix of the Reflection Equation algebra (modified or not), corresponding to a skew-invertible Hecke symmetry and define the generalized Harish-Chandra morphism in a similar way. We use this map in order to introduce quantum analogs of the so-called weight systems.