On a q-analog of the Wallach-Okounkov formula

Abstract

We obtain a $q$-analog of the well known Wallach-Okounkov result on a joint spectrum of invariant differential operators with polynomial coefficients on a prehomogeneous vector space of complex $n\times n$-matrices. We are motivated by applications to the problems of harmonic analysis in the quantum matrix ball: our main theorem can be used while proving the Plancherel formula (to be published). This paper is dedicated to our friend and colleague Dmitry Shklyarov who celebrates his 30-th birthday on April 8, 2006.

10 pages, corrected minor misprints

Cited by in corpus (3)

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• Quantized Weyl algebras, the double centralizer property, and a new First Fundamental Theorem for $U_q({\mathfrak{gl}}_n)$
• Plancherel formula for the quantum matrix ball - I