J Austral Math Soc Ser A 45 pp30--45, 1988.

Central Lacunary Sets for Lie Groups

A. H. Dooley

Abstract

If G is a compact connected Lie group every infinite subset ofÙG contains an infinite central L(p) set, for p < 2 + 2rank G/(dim G - rank G). A subset R ofÙG is of type central L(2) if and only if the associated set of characters on the maximal torus is of type L(2). The dual of a compact connected semisimple Lie group contains infinite sets which are central p-Sidon for all p > 1. Every infinite subset of the dual of SU(2) contains such a set.

1980 AMS Subject Classification: 42A44, 43A14

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Authors

A. H. Dooley

School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, N.S.W. 2033, Australia.