Spectral statistics along sequences of irreducible representations
Mathematical Physics
2007-05-23 v1 math.MP
Representation Theory
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).
Cite
@article{arxiv.math-ph/0702049,
title = {Spectral statistics along sequences of irreducible representations},
author = {IngolfSchäfer and Marek Ku\' s},
journal= {arXiv preprint arXiv:math-ph/0702049},
year = {2007}
}
Comments
14 pages, 1 figure