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

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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