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• W2953202330 abstract "Let M be a compact Kahler manifold equipped with a Hamiltonian action of a compact Lie group G. In this paper, we study the geometric quantization of the symplectic quotient M//G. Guillemin and Sternberg [Invent. Math. 67 (1982), 515--538] have shown, under suitable regularity assumptions, that there is a natural invertible map between the quantum Hilbert space over M//G and the G-invariant subspace of the quantum Hilbert space over M. We prove that in general the natural map of Guillemin and Sternberg is not unitary, textit{even to leading order in Planck's constant}. We then modify the quantization procedure by the metaplectic correction and show that in this setting there is still a natural invertible map between the Hilbert space over M//G and the G-invariant subspace of the Hilbert space over M. We then prove that this modified Guillemin--Sternberg map is asymptotically unitary to leading order in Planck's constant." @default.
• W2953202330 created "2019-06-27" @default.
• W2953202330 creator A5018733232 @default.
• W2953202330 creator A5074529493 @default.
• W2953202330 date "2006-09-29" @default.
• W2953202330 modified "2023-09-27" @default.
• W2953202330 title "Unitarity in quantization commutes with reduction" @default.
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• W2953202330 hasPublicationYear "2006" @default.
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