Let M be a connected d-dimensional complex projective manifold, and let A be a holomorphic positive Hermitian line bundle on M, with normalized curvature. Let G be a compact and connected Lie group of dimension d(G), and let T be a compact torus T of dimension d(T). Suppose that both G and T act on M in a holomorphic and Hamiltonian manner, that the actions commute, and linearize to A. If X is the principal circle-bundle associated to A, then this set-up determines commuting unitary representations of G and T on the Hardy space H(X) of X, which may then be decomposed over the irreducible representations of the two groups. If the moment map for the T-action is nowhere zero, all isotypical components for the torus are finite-dimensional, and thus provide a collection of finite-dimensional G-modules. Given a non-zero integral weight n(T) for T, we consider the isotypical components associated to the multiples kn(T), k that goes to infinity, and focus on how their structure as G-modules is reflected by certain local scaling asymptotics on X (and M). More precisely, given a fixed irreducible character n(G) of G, we study the local scaling asymptotics of the equivariant Szegő projectors associated to n(G) and kn(T), for k that goes to infinity, investigating their asymptotic concentration along certain loci defined by the moment maps.
(2015). Scaling asymptotics of Szego kernels under commuting Hamiltonian actions. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2015).
Scaling asymptotics of Szego kernels under commuting Hamiltonian actions
CAMOSSO, SIMONE
2015
Abstract
Let M be a connected d-dimensional complex projective manifold, and let A be a holomorphic positive Hermitian line bundle on M, with normalized curvature. Let G be a compact and connected Lie group of dimension d(G), and let T be a compact torus T of dimension d(T). Suppose that both G and T act on M in a holomorphic and Hamiltonian manner, that the actions commute, and linearize to A. If X is the principal circle-bundle associated to A, then this set-up determines commuting unitary representations of G and T on the Hardy space H(X) of X, which may then be decomposed over the irreducible representations of the two groups. If the moment map for the T-action is nowhere zero, all isotypical components for the torus are finite-dimensional, and thus provide a collection of finite-dimensional G-modules. Given a non-zero integral weight n(T) for T, we consider the isotypical components associated to the multiples kn(T), k that goes to infinity, and focus on how their structure as G-modules is reflected by certain local scaling asymptotics on X (and M). More precisely, given a fixed irreducible character n(G) of G, we study the local scaling asymptotics of the equivariant Szegő projectors associated to n(G) and kn(T), for k that goes to infinity, investigating their asymptotic concentration along certain loci defined by the moment maps.File | Dimensione | Formato | |
---|---|---|---|
phd_unimib_760816.pdf
accesso aperto
Descrizione: Tesi dottorato
Tipologia di allegato:
Doctoral thesis
Dimensione
614.04 kB
Formato
Adobe PDF
|
614.04 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.