2022/11/07 by Letzter, Gail, Sahi, Siddhartha, Salmasian, Hadi
#17B37 #20G42 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2211.03838
We introduce and study quantum Capelli operators inside newly constructed quantum Weyl algebras associated to three families of symmetric pairs. 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.