Generalized Harish-Chandra morphism on Reflection Equation algebras
Quantum Algebra
2025-01-07 v2
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.
Cite
@article{arxiv.2411.01303,
title = {Generalized Harish-Chandra morphism on Reflection Equation algebras},
author = {Dimitry Gurevich and Pavel Saponov},
journal= {arXiv preprint arXiv:2411.01303},
year = {2025}
}
Comments
Minor changes: some typos were corrected