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A structural criterion for the existence of infinite central $ \Lambda(p)$ sets


Authors: Kathryn E. Hare and David C. Wilson
Journal: Trans. Amer. Math. Soc. 337 (1993), 907-925
MSC: Primary 43A46; Secondary 43A80
DOI: https://doi.org/10.1090/S0002-9947-1993-1157613-2
MathSciNet review: 1157613
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Abstract: We classify the compact, connected groups which have infinite central $ \Lambda (p)$ sets, arithmetically characterize central $ \Lambda (p)$ sets on certain product groups, and give examples of $ \Lambda (p)$ sets which are non-Sidon and have unbounded degree. These sets are intimately connected with Figà-Talamanca and Rider's examples of Sidon sets, and stem from the existence of families of tensor product representations of almost simple Lie groups whose decompositions into irreducibles are rank-independent.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1157613-2
Keywords: $ \Lambda (p)$ set, lacunary set, representations of compact groups
Article copyright: © Copyright 1993 American Mathematical Society

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