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- W2003345810 abstract "Using the analytic assembly map that appears in the Baum–Connes conjecture in noncommutative geometry, we generalise the Guillemin–Sternberg conjecture that ‘quantisation commutes with reduction’ to (discrete series representations of) semisimple groups G with maximal compact subgroups K acting cocompactly on symplectic manifolds. We prove this generalised statement in cases where the image of the momentum map in question lies in the set of strongly elliptic elements g se ∗ , the set of elements of g ∗ with compact stabilisers. This assumption on the image of the momentum map is equivalent to the assumption that M = G × K N , for a compact Hamiltonian K -manifold N . The proof comes down to a reduction to the compact case. This reduction is based on a ‘quantisation commutes with induction’-principle, and involves a notion of induction of Hamiltonian group actions. This principle, in turn, is based on a version of the naturality of the assembly map for the inclusion K ↪ G ." @default.
- W2003345810 created "2016-06-24" @default.
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- W2003345810 date "2009-10-01" @default.
- W2003345810 modified "2023-09-27" @default.
- W2003345810 title "Quantisation commutes with reduction at discrete series representations of semisimple groups" @default.
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- W2003345810 doi "https://doi.org/10.1016/j.aim.2009.05.011" @default.
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