Quantisation commutes with reduction at discrete series representations of semisimple groups

DOI10.1016/j.aim.2009.05.011zbMath1193.22012arXiv0705.2956OpenAlexW2003345810MaRDI QIDQ843226

Peter Hochs

Publication date: 29 September 2009

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.2956

zbMATH Keywords

momentum mapmaximal compact subgroupsemisimple groupdiscrete series representation

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Semisimple Lie groups and their representations (22E46) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65)

Related Items (13)

An index theorem for higher orbital integrals ⋮ Geometric quantization for proper actions ⋮ Formal geometric quantisation for proper actions ⋮ An equivariant index for proper actions. III: The invariant and discrete series indices ⋮ Index of equivariant Callias-type operators and invariant metrics of positive scalar curvature ⋮ Positive scalar curvature and Poincaré duality for proper actions ⋮ Positive scalar curvature and an equivariant Callias-type index theorem for proper actions ⋮ A \(K\)-homological approach to the quantization commutes with reduction problem ⋮ Spin-structures and proper group actions ⋮ Geometric quantization and families of inner products ⋮ Orbital integrals and \(K\)-theory classes ⋮ Quantisation of presymplectic manifolds, $K$-theory and group representations ⋮ Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series

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