Suppose given a holomorphic and Hamiltonian action of a compact torus on a polarized Hodge manifold. Assume that the action lifts to the quantizing line bundle, so that there is an induced unitary representation of the torus on the associated Hardy space which decomposes into isotypes. The main result of this paper is the description of asymptotics along rays in weight space of traces of equivariant Toeplitz operators composed with quantomorphisms for the torus action. The main ingredient in the proof is the micro-local analysis of the equivariant Szego kernels. As a particular case we obtain a simple approach for asymptotics of the Lefschetz fixed point formula and traces of Toeplitz operators in the setting of ladder representations. We also consider equivariant asymptotic when the decomposition given by the standard circle action is taken into account, in this case one can recall previous results of X. Ma and W. Zhang or of R. Paoletti. We address some explicit computations for the action of the special unitary group of dimension two.

Galasso, A. (2022). Equivariant fixed point formulae and Toeplitz operators under Hamiltonian torus actions and remarks on equivariant asymptotic expansions. INTERNATIONAL JOURNAL OF MATHEMATICS, 33(2) [10.1142/s0129167x22500112].

Equivariant fixed point formulae and Toeplitz operators under Hamiltonian torus actions and remarks on equivariant asymptotic expansions

Galasso, A
2022

Abstract

Suppose given a holomorphic and Hamiltonian action of a compact torus on a polarized Hodge manifold. Assume that the action lifts to the quantizing line bundle, so that there is an induced unitary representation of the torus on the associated Hardy space which decomposes into isotypes. The main result of this paper is the description of asymptotics along rays in weight space of traces of equivariant Toeplitz operators composed with quantomorphisms for the torus action. The main ingredient in the proof is the micro-local analysis of the equivariant Szego kernels. As a particular case we obtain a simple approach for asymptotics of the Lefschetz fixed point formula and traces of Toeplitz operators in the setting of ladder representations. We also consider equivariant asymptotic when the decomposition given by the standard circle action is taken into account, in this case one can recall previous results of X. Ma and W. Zhang or of R. Paoletti. We address some explicit computations for the action of the special unitary group of dimension two.
Articolo in rivista - Articolo scientifico
Equivariant fixed point formulae; Equivariant Szego kernels; Equivariant Toeplitz operators; Hamiltonian torus actions;
English
15-gen-2022
2022
33
2
2250011
none
Galasso, A. (2022). Equivariant fixed point formulae and Toeplitz operators under Hamiltonian torus actions and remarks on equivariant asymptotic expansions. INTERNATIONAL JOURNAL OF MATHEMATICS, 33(2) [10.1142/s0129167x22500112].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/400114
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