Let $M$ be complex projective manifold, and $A$ a positive line bundle on it. Assume that $G=SU(2)$ acts on $M$ in a Hamiltonian manner, with nowhere vanishing moment map, and that this action linearizes to $A$. Then there is an associated unitary representation of $G$ on the associated algebro-geometric Hardy space, and the isotypical components are all finite dimensional. We consider the local and global asymptotic properties of the equivariant projector associated to a weight $k , oldsymbol{ u }$, when $oldsymbol{ u }$ is fixed and $k ightarrow +infty$.
Galasso, A., Paoletti, R. (2020). Equivariant Asymptotics of Szegő kernels under Hamiltonian SU(2)-actions. THE ASIAN JOURNAL OF MATHEMATICS, 24(3), 501-532 [10.4310/AJM.2020.v24.n3.a6].
Equivariant Asymptotics of Szegő kernels under Hamiltonian SU(2)-actions
Galasso, A.;Paoletti, R
2020
Abstract
Let $M$ be complex projective manifold, and $A$ a positive line bundle on it. Assume that $G=SU(2)$ acts on $M$ in a Hamiltonian manner, with nowhere vanishing moment map, and that this action linearizes to $A$. Then there is an associated unitary representation of $G$ on the associated algebro-geometric Hardy space, and the isotypical components are all finite dimensional. We consider the local and global asymptotic properties of the equivariant projector associated to a weight $k , oldsymbol{ u }$, when $oldsymbol{ u }$ is fixed and $k ightarrow +infty$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.