Toeplitz operators on CR manifolds and group actions

TL;DR

This paper investigates the algebraic structure of Toeplitz operators on compact CR manifolds with non-degenerate Levi curvature, establishing a star product for certain symbols and analyzing group-invariant operators under Lie group actions.

Contribution

It introduces a star product for Toeplitz operators on CR manifolds and explores the algebra of G-invariant Toeplitz operators under group actions.

Findings

Established a star product for symbols on CR manifolds.

Analyzed the algebra of G-invariant Toeplitz operators.

Extended Toeplitz operator theory to group action contexts.

Abstract

Let $(X, T^{1,0}X)$ be a connected orientable compact CR manifold of dimension $2n+1$, $n \geq 1$ with non-degenerate Levi curvature. In this paper, we study the algebra of Toeplitz operators on $X$ and we establish star product for some class of symbols on $X$. In the second part of this paper, we consider a compact locally free Lie group $G$ acting on $X$ and we investigate the associated algebra of $G$-invariant Toeplitz operators.