Orbital integrals and K-theory classes
| dc.contributor.author | Hochs, P. | |
| dc.contributor.author | Wang, H. | |
| dc.date.issued | 2019 | |
| dc.description.abstract | Let G be a semisimple Lie group with discrete series. We use maps K₀(C∗rG)→C defined by orbital integrals to recover group theoretic information about G, including information contained in K-theory classes not associated to the discrete series. An important tool is a fixed point formula for equivariant indices obtained by the authors in an earlier paper. Applications include a tool to distinguish classes in K₀(C∗rG), the (known) injectivity of Dirac induction, versions of Selberg’s principle in K-theory and for matrix coefficients of the discrete series, a Tannaka-type duality, and a way to extract characters of representations from K-theory. Finally, we obtain a continuity property near the identity element of G of families of maps K₀(C∗rG)→C, parametrised by semisimple elements of G, defined by stable orbital integrals. This implies a continuity property for L-packets of discrete series characters, which in turn can be used to deduce a (well-known) expression for formal degrees of discrete series representations from Harish-Chandra’s character formula. | |
| dc.description.statementofresponsibility | Peter Hochs and Hang Wang | |
| dc.identifier.citation | Annals of K-Theory, 2019; 4(2):185-209 | |
| dc.identifier.doi | 10.2140/akt.2019.4.185 | |
| dc.identifier.issn | 2379-1683 | |
| dc.identifier.issn | 2379-1691 | |
| dc.identifier.orcid | Hochs, P. [0000-0001-9232-2936] | |
| dc.identifier.uri | http://hdl.handle.net/2440/128691 | |
| dc.language.iso | en | |
| dc.publisher | Mathematical Sciences Publishers | |
| dc.relation.grant | http://purl.org/au-research/grants/arc/DE160100525 | |
| dc.rights | © 2019 Mathematical Sciences Publishers | |
| dc.source.uri | https://doi.org/10.2140/akt.2019.4.185 | |
| dc.subject | K-theory of group C*-algebras; orbital integral; equivariant index; semisimple Lie group; Connes–Kasparov conjecture | |
| dc.title | Orbital integrals and K-theory classes | |
| dc.type | Journal article | |
| pubs.publication-status | Published |