On a q-analog of the Wallach–Okounkov Formula

Abstract

We obtain a q-analog of the well-known result on a joint spectrum of invariant differential operators with polynomial coefficients on a prehomogeneous vector space of complex n × n-matrices. We are motivated by applications to the problems of harmonic analysis in the quantum matrix ball: our main theorem can be used to prove the Plancherel formula (to be published).