Plancherel formula for the quantum matrix ball - I

Details Plancherel formula for the quantum matrix ball - I Plancherel formula for the quantum matrix ball - I

2009-03-24

arxiv.org/abs/0903.4068v2

Mathematics

Quantum Algebra

24 pages, improved exposition

Scientific paper

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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