Plancherel Measure for the Quantum Matrix Ball-1 - Bershtein, O.; Kolisnyk, Ye. (Журнал математичної фізики, аналізу, геометрії, 2009)
The Plancherel formula is one of the celebrated results of harmonic analysis on semisimple Lie groups and their homogeneous spaces. The main goal of this work is to find a q-analogue of the Plancherel formula for spherical transform on the unit matrix ball. Here we present an explicit formula for the radial part of the Plancherel measure. The q-Jacobi polynomials as spherical functions naturally arise on the way. Mathematics Subject Classification: 81R50, 17B37, 20G42.