Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-04T21:25:06.150Z Has data issue: false hasContentIssue false
  • English
  • Français

Kazhdan constants for compact groups

Part of: Compact groups Locally compact groups and their algebras

Published online by Cambridge University Press:  09 April 2009

Markus Neuhauser
Markus Neuhauser
Affiliation:
Markus Neuhauser Department of Mathematics C, TU Graz, Steyrergasse 30/III, 8010 Graz, Austria e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that for the computation of the Kazhdan constant for a compact group only the regular representation restricted to the orthogonal complement of the constant functions needs to be taken into account.

MSC classification

Secondary: 22C05: Compact groups 22D10: Unitary representations of locally compact groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 1 , August 2006 , pp. 11 - 14
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Bacher, R. and de la Harpe, P., ‘Exact values of Kazhdan constants for some finite groups’, J. Algebra 163 (1994), 495–515.CrossRefGoogle Scholar
[2]Deutsch, A., Kazhdan's property (T) and related properties of locally compact and discrete groups (Ph.D. Thesis, University of Edinburgh, 1992).Google Scholar
[3]Deutsch, A., ‘Kazhdan constants for the circle’, Bull. London Math. Soc. 26 (1994), 459–464.CrossRefGoogle Scholar
[4]Deutsch, A. and Valette, A., ‘On diameters of orbits of compact groups in unitary representations’, J. Austral. Math. Soc. (Series A) 59 (1995), 308–312.CrossRefGoogle Scholar
[5]Dixmier, J., C*-algebras, North-Holland Math. Library 15 (North-Holland, Amsterdam, 1982).Google Scholar
[6]Folland, G. B., A course in abstract harmonic analysis, Studies in Advanced Mathematics (CRC Press, Boca Raton, FL, 1995).Google Scholar
[7]de Ia Harpe, P. and Valette, A., La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 175 (Société Mathématique de France, 1989).Google Scholar
[8]Kazhdan, D. A., ‘Connection of the dual space of a group with the structure of its close subgroups’, Funct. Anal. Appl. 1 (1967), 63–65.CrossRefGoogle Scholar
[9]Lubotzky, A., Discrete groups, expanding graphs and invariant measures, Progress in Mathematics 125 (Birkhäuser, Basel, 1994).CrossRefGoogle Scholar
[10]Lubotzky, A. and Pak, I., ‘The product replacement algorithm and Kazhdan's property (T)’, J. Amer Math. Soc. 14 (2000), 347–363.CrossRefGoogle Scholar
[11]Neuhauser, M., ‘Kazhdan constants for conjugacy classes of compact groups’, J. Algebra 270 (2003), 564–582.CrossRefGoogle Scholar
[12]Pak, I. and Zuk, A., ‘On Kazhdan constants and mixing of random walks’, Int. Math. Res. Not. 36 (2002), 1891–1905.CrossRefGoogle Scholar