Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-06-03T11:54:32.820Z Has data issue: false hasContentIssue false
  • English
  • Français

The size of characters of exceptional lie groups

Part of: Lie groups Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Kathryn E. Hare  and
Karen Yeats
Kathryn E. Hare
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada e-mail: kehare@uwaterloo.cakayeats@uwaterloo.ca
Karen Yeats
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada e-mail: kehare@uwaterloo.cakayeats@uwaterloo.ca
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.

Pointwise bounds for characters of representations of the compact, connected, simple, exceptional Life groups are obtained. It is a classical result that if μ is a central, continuous measure on such a group, then μdimG is absolutely continuous. Our estimates on the size of characters allow us to prove that the exponent, dimension of G, can be replaced by approximately the rank of G. Similar results were obtained earlier for the classical, compact Lie groups.

Keywords

compactexceptional Lie groupcharacterscentral measures

MSC classification

Secondary: 22E46: Semisimple Lie groups and their representations 43A80: Analysis on other specific Lie groups 43A65: Representations of groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 2 , October 2004 , pp. 233 - 248
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Brocker, T. and Dieck, T., Representations of compact Lie groups (Springer, New York, 1985).CrossRefGoogle Scholar
[2]Hare, K., ‘The size of characters of compact Lie groups’, Studia Math. 129 (1998), 1–18.CrossRefGoogle Scholar
[3]Hare, K., Wilson, D. and Yee, W. L., ‘Pointwise estimates of the size of characters of compact Lie groups’, J. Austral. Math. Soc. 69 (2000), 61–84.CrossRefGoogle Scholar
[4]Humphreys, J., Introduction to Lie algebras and representation theory (Springer, New York, 1972).CrossRefGoogle Scholar
[5]Humphreys, J., Reflection groups and Coxeter groups, Cambridge Stud. Adv. Math. 29 (Cambridge University Press, Cambridge, 1990).CrossRefGoogle Scholar
[6]Mirmura, M. and Toda, H., Topology of Lie groups, Transl. Math. Monographs 91 (Amer. Math. Soc., Providence, 1991).Google Scholar
[7]Ragozin, D., ‘Central measures on compact simple Lie groups’, J. Funct. Anal. 10 (1972), 212–229.CrossRefGoogle Scholar
[8]Ricci, F. and Stein, E. M., ‘Harmonic analysis on nilpotent groups and singular integrals. III. Fractional integration along manifolds’, J. Funct. Anal. 86 (1989), 360–389.CrossRefGoogle Scholar
[9]Ricci, F. and Travaglini, G., ‘L p – L q estimates for orbital measures and Radon transform on compact Lie groups and Lie algebras’, J. Funct. Anal. 129 (1995), 132–147.CrossRefGoogle Scholar
[10]Rider, D., ‘Central lacunary sets’, Monatsh. Math. 76 (1972), 328–338.Google Scholar
[11]Varadarajan, V., Lie groups, Lie algebras and their representations (Springer, New York, 1984).CrossRefGoogle Scholar