On the number of irreducible representations of degree ≤𝑛 of a Lie group

Rothaus, O. S.

doi:10.1090/S0002-9939-1975-0382550-5

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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On the number of irreducible representations of degree $\leq n$ of a Lie group
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by O. S. Rothaus PDF

Proc. Amer. Math. Soc. 51 (1975), 217-220 Request permission

Abstract:

We give a proof of part of a result of Robert Cahn [1] on the asymptotic behavior of the number of irreducible representations of degree $\leq n$ of a semisimple Lie group. The argument is a general one and does not depend on classification.

References

Robert S. Cahn, Lattice points and Lie groups. I, II, Trans. Amer. Math. Soc. 183 (1973), 119–129; ibid. 183 (1973), 131–137. MR 335687, DOI 10.1090/S0002-9947-1973-0335687-3
O. S. Rothaus, The volume of a region defined by polynomial inequalities, Proc. Amer. Math. Soc. 42 (1974), 265–267. MR 331219, DOI 10.1090/S0002-9939-1974-0331219-0