Geodesic
Plancherel measure for the quantum matrix ball-1
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009), pp. 315-346.

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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. 
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O. Bershtein; Ye. Kolisnyk. Plancherel measure for the quantum matrix ball-1. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009), pp. 315-346. http://geodesic.mathdoc.fr/item/JMAG_2009_5_a0/

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