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Type: Journal article
Title: The ring structure of twisted equivariant KK-theory for noncompact Lie groups
Author: Fok, C.-K.
Varghese, M.
Citation: Communications in Mathematical Physics, 2021; 385(2):633-666
Publisher: Springer-Verlag
Issue Date: 2021
ISSN: 0010-3616
Statement of
Chi-Kwong Fok, Varghese Mathai
Abstract: Let G be a connected semisimple Lie group with its maximal compact subgroup K being simply-connected. We show that the twisted equivariant KK-theory KK∙G(G/K,τGG) of G has a ring structure induced from the renowned ring structure of the twisted equivariant K-theory K∙K(K,τKK) of a maximal compact subgroup K. We give a geometric description of representatives in KK∙G(G/K,τGG) in terms of equivalence classes of certain equivariant correspondences and obtain an optimal set of generators of this ring. We also establish various properties of this ring under some additional hypotheses on G and give an application to the quantization of q-Hamiltonian G-spaces in an appendix. We also suggest conjectures regarding the relation to positive energy representations of LG that are induced from certain unitary representations of G in the noncompact case.
Description: Published online: 14 June 2021
Rights: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
DOI: 10.1007/s00220-021-04131-w
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