Lattice points and Lie groups. I
Abstract: Assume that G is a compact semisimple Lie group and 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 , where a = the rank of and b = the number of positive roots of .
-  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