We define conic reductions Xνred for torus actions on the boundary X of a strictly pseudo-convex domain and for a given weight ν labeling a unitary irreducible representation. There is a natural residual circle action on Xνred . We have two natural decompositions of the corresponding Hardy spaces H(X) and H(Xνred) . The first one is given by the ladder of isotypes H(X) kν , k∈ Z ; the second one is given by the k-th Fourier components H(Xνred)k induced by the residual circle action. The aim of this paper is to prove that they are isomorphic for k sufficiently large. The result is given for spaces of (0, q)-forms with L2 -coefficient when X is a CR manifold with non-degenerate Levi form.

Galasso, A. (2024). Commutativity of quantization with conic reduction for torus actions on compact CR manifolds. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 65(1 (February 2024)), 1-16 [10.1007/s10455-023-09931-y].

Commutativity of quantization with conic reduction for torus actions on compact CR manifolds

Galasso, A
2024

Abstract

We define conic reductions Xνred for torus actions on the boundary X of a strictly pseudo-convex domain and for a given weight ν labeling a unitary irreducible representation. There is a natural residual circle action on Xνred . We have two natural decompositions of the corresponding Hardy spaces H(X) and H(Xνred) . The first one is given by the ladder of isotypes H(X) kν , k∈ Z ; the second one is given by the k-th Fourier components H(Xνred)k induced by the residual circle action. The aim of this paper is to prove that they are isomorphic for k sufficiently large. The result is given for spaces of (0, q)-forms with L2 -coefficient when X is a CR manifold with non-degenerate Levi form.
Articolo in rivista - Articolo scientifico
CR conic reduction; Hardy space; Torus action;
English
29-nov-2023
2024
65
1 (February 2024)
1
16
4
none
Galasso, A. (2024). Commutativity of quantization with conic reduction for torus actions on compact CR manifolds. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 65(1 (February 2024)), 1-16 [10.1007/s10455-023-09931-y].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/453800
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