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Generalized Harish-Chandra morphism on Reflection Equation algebras
Journal of Geometry and Physics. 2025. Vol. 210. Article 105435.
Gurevich D., Сапонов П. А.
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 Reflflection Equation algebras. To this end we introduce the eigenvalues of the generating matrix of the Reflflection Equation algebra (modifified or not), corresponding to a skew-invertible Hecke symmetry and defifine
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.