Suppose that a compact and connected Lie group G acts on a complex Hodge manifold M in a holomorphic and Hamiltonian manner, and that the action linearizes to a positive holomorphic line bundle A on M. Then there is an induced unitary representation on the associated Hardy space and, if the moment map of the action is nowhere vanishing, the corresponding isotypical components are all finite dimensional. We study the asymptotic concentration behavior of the corresponding equivariant Szegö kernels near certain loci defined by the moment map.

Paoletti, R. (2022). Szegö kernel equivariant asymptotics under Hamiltonian Lie group actions. THE JOURNAL OF GEOMETRIC ANALYSIS, 32(4 (April 2022)) [10.1007/s12220-021-00829-4].

Szegö kernel equivariant asymptotics under Hamiltonian Lie group actions

Paoletti R.
2022

Abstract

Suppose that a compact and connected Lie group G acts on a complex Hodge manifold M in a holomorphic and Hamiltonian manner, and that the action linearizes to a positive holomorphic line bundle A on M. Then there is an induced unitary representation on the associated Hardy space and, if the moment map of the action is nowhere vanishing, the corresponding isotypical components are all finite dimensional. We study the asymptotic concentration behavior of the corresponding equivariant Szegö kernels near certain loci defined by the moment map.
Articolo in rivista - Articolo scientifico
Hamiltonian action; Hardy space; Moment map; Scaling asymptotics; Szego kernel;
English
Paoletti, R. (2022). Szegö kernel equivariant asymptotics under Hamiltonian Lie group actions. THE JOURNAL OF GEOMETRIC ANALYSIS, 32(4 (April 2022)) [10.1007/s12220-021-00829-4].
Paoletti, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/352158
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