2024/12/17 by Dimitri Gurevich, Pavel Saponov, Gurevich, Dimitri +3 · 1 citation
Mathematics · #17B37 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Numerical methods for differential equations #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2412.13373
openalex publication_date 2024/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum differential operators on Reflection Equation Algebras, corresponding to Hecke symmetries R were introduced in previous publications. In the present paper we are mainly interested in quantum analogs of the Laplace and Casimir operators, which are invariant with respect to the action of the Quantum Groups Uq(sl(N)), provided R is the Drinfeld-Jimbo R-matrix. We prove that any such an operator maps the central characteristic subalgebra of a Reflection Equation algebra into itself. Also, we define the notion of normal ordering for the quantum differential operators and prove an analog of the Wick theorem for the product of partially ordered operators. As an important corollary we find a set of universal matrix Capelli identities generalizing the results of [Ok2] and [JLM]. Besides, we prove that the normal ordered form of any central differential operator from the characteristic subalgebra is also a central differential operator.