The Capelli eigenvalue problem for quantum groups
Quantum Algebra
2024-05-27 v2 Combinatorics
Representation Theory
Abstract
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.
Cite
@article{arxiv.2211.03838,
title = {The Capelli eigenvalue problem for quantum groups},
author = {Gail Letzter and Siddhartha Sahi and Hadi Salmasian},
journal= {arXiv preprint arXiv:2211.03838},
year = {2024}
}