Resumen de The Capelli eigenvalue problem for quantum groups

Gail Letzter, Siddhartha Sahi, Hadi Salmasian

• We introduce and study quantum Capelli operators inside newly constructed quantum Weyl algebras associated to three families of symmetric pairs (Letzter et al. in J Algebra, 2024). Both the center of a particular quantized enveloping algebra and the Capelli operators act semisimply on the polynomial part of these quantum Weyl algebras. We show how to transfer well-known properties of the center arising from the theory of quantum symmetric pairs to the Capelli operators. Using this information, we provide a natural realization of Knop-Sahi interpolation polynomials as functions that produce eigenvalues for quantum Capelli operators.