Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 021, 30 pages      arXiv:0902.3628
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

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.

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