Applications of the Capelli identities in physics and representation theory

David J. Rowe

Published 2015-01-10Version 1

Capelli identities are shown to facilitate the construction of representations of various Heisenberg algebras that arise in many-particle quantum mechanics and the construction of holomorphic representations of many Lie algebras by Vector Coherent State methods. We consider the original Capelli identity and its generalizations by Turnbull and by Howe and Umeda.