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arXiv · 0903.4068

Plancherel formula for the quantum matrix ball - I

O. Bershtein·Ye. Kolisnyk
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Abstract

Plancherel formula is one of the celebrated result of harmonic analysis on semisimple Lie groups and their homogeneous spaces. The main goal of this work is to find a q-analog of the Plancherel formula for spherical transform the unit matrix ball. Here we present an explicit formula for the radial part of the Plancherel measure. q-Jacobi polynomials as spherical functions naturally arise on the way.

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O. Bershtein, Ye. Kolisnyk. 2009-10-13. Plancherel formula for the quantum matrix ball - I. https://arxiv.org/abs/0903.4068

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