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Spectral statistics along sequences of irreducible representations

Ingolf Schäfer·Marek Kuś
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Abstract

We discuss the nearest neighbor distribution of the eigenvalues for hermitian generators in the Lie algebra of a semisimple complex Lie Group along a sequence of irreducible representations. After the basic definitions a limit theorem for rays of irreducible representation is formulated. Then it is proved that only a certain kind of rescaling will give meaning full results in the general case. Finally, we give explicit formulas for the Lipkin operator in the case of SU(3).

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Ingolf Schäfer, Marek Kuś. 2007-02-14. Spectral statistics along sequences of irreducible representations. https://arxiv.org/abs/math-ph/0702049

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