Toeplitz Quantization and Asymptotic Expansions: Geometric Construction
Miroslav Englis, Harald Upmeier

TL;DR
This paper introduces a geometric method for constructing invariant differential operators on symmetric domains, providing an asymptotic expansion framework analogous to star-products in quantization of Kähler manifolds.
Contribution
It develops the concept of star-restriction as a real analogue of star-products and offers a geometric construction for invariant differential operators on symmetric domains.
Findings
Defined star-restriction for symmetric domains
Constructed invariant differential operators geometrically
Established asymptotic expansion framework
Abstract
For a real symmetric domain , with complexification , we introduce the concept of "star-restriction" (a real analogue of the "star-products" for quantization of K\"ahler manifolds) and give a geometric construction of the -invariant differential operators yielding its asymptotic expansion.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology
