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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     author = {O. Bershtein and Ye. Kolisnyk},
     title = {Plancherel measure for the quantum matrix ball-1},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {315--346},
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     volume = {5},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2009_5_a0/}
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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/