English

Plancherel formula for the quantum matrix ball - I

Quantum Algebra 2009-10-13 v2 Representation Theory

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.

Keywords

Cite

@article{arxiv.0903.4068,
  title  = {Plancherel formula for the quantum matrix ball - I},
  author = {O. Bershtein and Ye. Kolisnyk},
  journal= {arXiv preprint arXiv:0903.4068},
  year   = {2009}
}

Comments

24 pages, improved exposition

R2 v1 2026-06-21T12:43:46.377Z