Quantization of the coadjoint orbits of a compact Lie group (Q1851394)

Given a Kähler manifold, on the quantum Hilbert space \(\mathcal H\) arising from Kähler quantization, the Berezin symbol of a bounded linear operator is defined via coherent states and composition of operators; it induces a star product on the space of Berezin symbols. Given an irreducible representation \(V\) of a compact, connected, and simply connected Lie group \(G\) having highest weight vector \(v \in V\), its momentum mapping \(\Phi: \text P(V) \to\mathbf g^*\) identifies the \(G\)-orbit of \([v]\) in \(\text P(V)\) with the corresponding coadjoint orbit. In the paper, Berezin's symbolic calculus on that coadjoint orbit is related with Berezin's calculus on \(\text P(V)\).