Speaker : 沈威銓 (University of Cologne)
Title : Asymptotics of torus equivariant Szeg? kernel on a compact CR manifold.
Time : 2020-02-07 (Fri) 10:30 - 12:00
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: In this talk, we consider a compact CR manifold $(X,T^{1,0}X)$ of dimension $2n+1$, $n\geq 2$, admitting a $S^1\times T^d$ action. We fix the lattice point $(p_1,\cdots,p_d)\in\mathbb{Z}^{d}$ satisfying $(-p_1,\cdots,-p_d)$ is a regular value of the associate CR moment map $\mu$ and study the asymptotic expansion of the corresponding torus equivariant Szegő kernel $\Pi^{(0)}_{m,mp_1,\cdots,mp_d}(x,y)$ as $m\to +\infty$ under certain assumptions on $Y:=\mu^{-1}(-p_1,\cdots,-p_d)$. As a corollary, we find a condition when the space of $R$-equivariant CR functions on a irregular Sasakian manifold is non-trivial in semi-classical limit.