Preprint Article Version 1 This version is not peer-reviewed

# Convexity and Toeplitz Quantization: Kostant's Theorem for the symplectomorphism group of the sphere

Version 1 : Received: 28 February 2019 / Approved: 1 March 2019 / Online: 1 March 2019 (12:25:47 CET)

How to cite: Hadrami Bouleryah, M.L. Convexity and Toeplitz Quantization: Kostant's Theorem for the symplectomorphism group of the sphere. Preprints 2019, 2019030010 (doi: 10.20944/preprints201903.0010.v1). Hadrami Bouleryah, M.L. Convexity and Toeplitz Quantization: Kostant's Theorem for the symplectomorphism group of the sphere. Preprints 2019, 2019030010 (doi: 10.20944/preprints201903.0010.v1).

## Abstract

In this paper we use Toeplitz quantization to extend in a very natural way Kostant's theorem for the group $SU(m)$ to the group of symplectomorphisms of the unit sphere and we also give another proof of the infinite dimensional version of Schur and Horn theorem for the sphere based on Schur and Horn theorem for Hermitian matrices.

## Subject Areas

Toeplitz quantization, decreasing rearrangement, majorization, spectral measure, measure preserving transformation, Hermitian matrices