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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Lattice points and Lie groups. I
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by Robert S. Cahn PDF
Trans. Amer. Math. Soc. 183 (1973), 119-129 Request permission

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
  • Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), 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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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 183 (1973), 119-129
  • MSC: Primary 22E45
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0335687-3
  • MathSciNet review: 0335687