Spectral statistics along sequences of irreducible representations

2007/02/14 by Schäfer, Ingolf, Kuś, Marek
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math-ph/0702049

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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