Toeplitz operators on CR manifolds and group actions
Aula: Aula 25 and online - Ore: 10.00
Via della Garzetta 48, Brescia
Mauro SPERA, Università Cattolica del Sacro Cuore
National Center for Theoretical Sciences (NCTS), Mathematics Division, Taiwan
Let X be a compact connected orientable CR manifold with non-degenerate Levi curvature. We define Toeplitz operators acting on spaces of (0,q)-forms with L^2 coefficients and we study their algebra. When X is the circle bundle of a quantizable symplectic manifold, we show that the algebra of Toeplitz operators defines a deformation of the Poisson algebra of smooth functions on the symplectic manifold. Given a locally free action of a compact connected Lie group G, we study the associated algebra of G-invariant Toeplitz operators for (0,q)-forms. In the presence of a locally free transversal CR circle action, we study Fourier components of Toeplitz operators. We recovered well-known theorems for G-invariant Toeplitz operators on circle bundles of quantizable Kaehler manifolds.
This is based on joint works with Chin-Yu Hsiao.