Toeplitz Quantization and Asymptotic Expansions: Geometric Construction

Abstract

For a real symmetric domain $G_{\mathbb{R}}/K_{\mathbb{R}}$, with complexification $G_{\mathbb{C}}/K_{\mathbb{C}}$, 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 $G_{\mathbb{R}}$-invariant differential operators yielding its asymptotic expansion.