Submitted:
28 February 2019
Posted:
01 March 2019
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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.
Keywords:
Toeplitz quantization
; decreasing rearrangement
; majorization
; spectral measure
; measure preserving transformation
; Hermitian matrices
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