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

2021/10/14 by Galasso, Andrea
#Complex Variables (math.CV) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2110.07104

Abstract

We define conic reduction X^red_ν 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 X^red_ν. We have two natural decompositions of the corresponding Hardy spaces H(X) and H(X^red_ν). 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(X^red_ν)_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-curvature.

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