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
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