Applications of the Capelli identities in physics and representation theory. (12th January 2015)

• Record Type: Journal Article
• Authors: Rowe, D J
• Is Part Of: Journal of physics. Volume 48:Number 5(2015)
• Publication Date: 2015-01-12
• Subjects: Capelli identities -- group contraction -- vector coherent state theory -- induced representations -- holomorphic representations -- Pfaffians; 02 -- 20.-a -- 02.20.Qs; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/5/055203
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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.