Duality of spectral curves arising in two-matrix models
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The two matrix model is considered, with measure given by the exponential of a sum of polynomials in two different variables. It is shown how to derive a sequence of pairs of ``dual'' finite size systems of ODEs for the corresponding biorthonormal polynomials. An inverse theorem is proved showing how to reconstruct such measures from pairs of semi-infinite finite band matrices defining the recursion relations and satisfying the string equation. A proof is given in the $N\to \infty$ limit that the dual systems obtained share the same spectral curve.
Write-up based on lecture by J. Harnad given at NEEDS 2001 Euroconference Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K. July 24-31, 2001
Write-up based on lecture by J. Harnad given at NEEDS 2001 Euroconference Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K. July 24-31, 2001