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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Lattice points and Lie groups. I

Author: Robert S. Cahn
Journal: Trans. Amer. Math. Soc. 183 (1973), 119-129
MSC: Primary 22E45
MathSciNet review: 0335687
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Abstract: Assume that G is a compact semisimple Lie group and $ \mathfrak{G}$ its associated Lie algebra. It is shown that the number of irreducible representations of G of dimension less than or equal to n is asymptotic to $ k{n^{a/b}}$, where a = the rank of $ \mathfrak{G}$ and b = the number of positive roots of $ \mathfrak{G}$.

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PII: S 0002-9947(1973)0335687-3
Keywords: Semisimple Lie group, irreducible representation, lattice points, Weyl's character formula
Article copyright: © Copyright 1973 American Mathematical Society