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SIGMA 5 (2009), 021, 30 pages arXiv:0902.3628
https://doi.org/10.3842/SIGMA.2009.021
Contribution to the Special Issue on Deformation Quantization
Toeplitz Quantization and Asymptotic Expansions: Geometric Construction
Miroslav Englis a, b and Harald Upmeier c
a) Mathematics Institute, Silesian University at Opava,
Na Rybnícku 1, 74601 Opava, Czech Republic
b) Mathematics Institute, Zitná 25, 11567 Prague 1, Czech Republic
c) Fachbereich Mathematik, Universität Marburg, D-35032 Marburg, Germany
Received October 01, 2008, in final form February 14, 2009; Published online February 20, 2009
Abstract
For a real symmetric domain GR/KR, with complexification
GC/KC, we introduce the concept of ''star-restriction'' (a real
analogue of the ''star-products'' for quantization of Kähler manifolds)
and give a geometric construction of the GR-invariant differential
operators yielding its asymptotic expansion.
Key words:
bounded symmetric domain; Toeplitz operator; star product; covariant quantizationn.
pdf (383 kb)
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