caa a22 4500 445836644 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0755-9 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0755-9 Kirwin William Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal aut Higher asymptotics of unitarity in "quantization commutes with reduction” [Elektronische Daten] [William Kirwin] Let M be a compact Kähler manifold equipped with a Hamiltonian action of a compact Lie group G. Guillemin and Sternberg (Invent Math 67:515-538, 1982, no. 3), showed that there is a geometrically natural isomorphism between the G-invariant quantum Hilbert space over M and the quantum Hilbert space over the symplectic quotient M //G. This map, though, is not in general unitary, even to leading order in $${\hslash}$$ . Hall and Kirwin (Commun Math Phys 275:401-422, 2007, no. 2), showed that when the metaplectic correction is included, one does obtain a map which, while not in general unitary for any fixed $${\hslash}$$ , becomes unitary in the semiclassical limit $${\hslash\rightarrow0}$$ (cf. the work of Ma and Zhang (C R Math Acad Sci Paris 341:297-302, 2005, no. 5), and (Astérisque No. 318:viii+154, 2008). The unitarity of the classical Guillemin-Sternberg map and the metaplectically corrected analogue is measured by certain functions on the symplectic quotient M //G. In this paper, we give precise expressions for these functions, and compute complete asymptotic expansions for them as $${\hslash\rightarrow0}$$ . Springer-Verlag, 2010 Geometric quantization nationallicence Symplectic reduction nationallicence Asymptotic expansion nationallicence Laplace's method nationallicence Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 647-662 0025-5874 269:3-4<647 2011 269 209 https://doi.org/10.1007/s00209-010-0755-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0755-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kirwin William Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 647-662 0025-5874 269:3-4<647 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer