Let X be the circle bundle associated to a positive line bundle on a complex projective (or, more generally, compact symplectic) manifold. The Tian-Zelditch expansion on X may be seen as a local manifestation of the decomposition of the (generalized) Hardy space H(X) into isotypes for the S 1-action. More generally, given a compatible action of a compact Lie group, and under general assumptions guaranteeing finite dimensionality of isotypes, we may look for asymptotic expansions locally reflecting the equivariant decomposition of H(X) over the irreducible representations of the group. We focus here on the case of compact tori

Paoletti, R. (2012). Asymptotics of Szegö kernels under Hamiltonian torus actions. ISRAEL JOURNAL OF MATHEMATICS, 191(1), 363-403 [10.1007/s11856-011-0212-4].

Asymptotics of Szegö kernels under Hamiltonian torus actions

PAOLETTI, ROBERTO
2012

Abstract

Let X be the circle bundle associated to a positive line bundle on a complex projective (or, more generally, compact symplectic) manifold. The Tian-Zelditch expansion on X may be seen as a local manifestation of the decomposition of the (generalized) Hardy space H(X) into isotypes for the S 1-action. More generally, given a compatible action of a compact Lie group, and under general assumptions guaranteeing finite dimensionality of isotypes, we may look for asymptotic expansions locally reflecting the equivariant decomposition of H(X) over the irreducible representations of the group. We focus here on the case of compact tori
Articolo in rivista - Articolo scientifico
Szego kernels, torus actions, isotypical decompositions, local scaling asymptotics
English
21-dic-2011
2012
191
1
363
403
none
Paoletti, R. (2012). Asymptotics of Szegö kernels under Hamiltonian torus actions. ISRAEL JOURNAL OF MATHEMATICS, 191(1), 363-403 [10.1007/s11856-011-0212-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/44583
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