Non-perturbative Deformation Quantization of Cartan Domains

✍ Scribed by D. Borthwick; A. Lesniewski; H. Upmeier

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 664 KB
• Volume: 113
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1993.1050

✦ Synopsis

We construct families of non-commuting (\mathbb{C}^{*})-algebras of "quantized functions" for bounded irreducible Hermitian symmetric spaces. For this procedure, we use algebras of Toeplitz operators defined with respect to a perturbation of the ordinary Bergman metric. We prove the deformation quantization conditions for these algebras. 1993 Academic Press, Inc.