Invariant star products and representations of compact semisimple Lie groups
type: Item
instance of: scholarly article
title: Invariant star products and representations of compact semisimple Lie groups
zbMATH Open document ID: 0681.53036
DOI: 10.1007/BF00416512
published in: Letters in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: Starting from the work of \textit{F. A. Berezin} [Izv. Akad. Nauk SSSR, Ser. Mat. 39, 363-402 (1975; Zbl 0312.53050)] an earlier paper by the author [Lett. Math. Phys. 11, 361-372 (1986; Zbl 0618.53049)] defined an invariant star product on every nonexceptional Kähler symmetric space. A recursion formula is obtained to calculate the corresponding invariant Hochschild 2-cochains for spaces of types II and III. An invariant star product is defined on every integral symplectic (Kähler) homogeneous space of simply-connected compact Lie groups (on every integral orbit of the coadjoint representation). The invariant 2-cochains are obtained from the Bochner-Calabi function of the space. The leading term of the \(\ell th\)-2-cochain is determined by the \(\ell\)-power of the Laplace operator.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 4115466
zbMATH Keywords: invariant star product
zbMATH Keywords: Kähler symmetric space
zbMATH Keywords: homogeneous space
zbMATH Keywords: Bochner-Calabi function
zbMATH Keywords: Laplace operator
Wikidata QID: Q115395014
author: Carlos Moreno
MaRDI profile type: Publication
cites work: Déformation du crochet de Poisson sur une variété symplectique
cites work: Deformation theory and quantization. I: Deformations of symplectic structures
cites work: Some ideas about quantization
cites work: *-products on some Kähler manifolds
cites work: *-products on \(D^ 1(C)\), \(S^ 2\) and related spectral analysis
cites work: A note on coherent state representations of Lie groups
cites work: Regular * representations of Lie algebras
cites work: Q3849170
cites work: The stationary phase method and pseudodifferential operators
cites work: Kählerian Coset Spaces of Semisimple Lie Groups
cites work: Isometric imbedding of complex manifolds
cites work: Coherent states for arbitrary Lie group
cites work: COHERENT STATES AND KAHLER MANIFOLDS
cites work: Nilpotent Fourier transform and applications
cites work: An associative algebra of functions on the orbits of nilpotent Lie groups
cites work: Invariant *-products of holomorphic functions on the hyperbolic Hermitian spaces
full work available at URL: https://doi.org/10.1007/bf00416512
OpenAlex ID: W2067359976
description: scientific article; zbMATH DE number 4115466