Multiplicities of compact Lie group representations via Berezin quantization. (English) Zbl 1199.22016

Cahen, Benjamin

Mat. Vesn. 60, No. 4, 295-309 (2008).

Let \(G\) be a compact Lie group and \(\pi\) be a unitary representation of \(G\) on a reproducing kernel Hilbert space. The author studies the application of Berezin quantization to the description of the irreducible decomposition of \(\pi\). The integral formulas for the multiplicity of weights as well as illustrative examples of the method to the Gelfand pairs in the case of the action of the unitary group \(U(n)\) on the \((2n+1)\)-dimensional Heisenberg group are given.

Reviewer: Božidar Jovanović (Beograd)

MSC:

22E46	Semisimple Lie groups and their representations
46E22	Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)

Keywords:

decomposition of unitary representation; Berezin symbol; flag manifold; semisimple compact Lie group