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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 $\mathfrak {G}$.

References [Enhancements On Off] (What's this?)

  • Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR 0143793
  • Jean-Pierre Serre, Algèbres de Lie semi-simples complexes, W. A. Benjamin, inc., New York-Amsterdam, 1966 (French). MR 0215886

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Keywords: Semisimple Lie group, irreducible representation, lattice points, Weyl’s character formula
Article copyright: © Copyright 1973 American Mathematical Society