• Corpus ID: 119601092

Howe pairs, supersymmetry, and ratios of random characteristic polynomials for the unitary groups U(N)

@article{Conrey2005HowePS,
  title={Howe pairs, supersymmetry, and ratios of random characteristic polynomials for the unitary groups U(N)},
  author={J. Brian Conrey and David W. Farmer and Martin R. Zirnbauer},
  journal={arXiv: Mathematical Physics},
  year={2005}
}
For the classical compact Lie groups K = U(N) the autocorrelation functions of ratios of random characteristic polynomials are studied. Basic to our treatment is a property shared by the spinor representation of the spin group with the Shale-Weil representation of the metaplectic group: in both cases the character is the analytic square root of a determinant or the reciprocal thereof. By combining this fact with Howe's theory of supersymmetric dual pairs (g,K), we express the K-Haar average… 
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