Virasoro generators and bilinear equations for isomonodromic tau functions
John Harnad
Abstract: It is shown how the bilinear differential equations satisfied
by Fredholm determinants of integral operators appearing as spectral
distribution functions for random matrices may be deduced from the associated
systems of nonautonomous Hamiltonian equations satisfied by auxiliary canonical
phase space variables introduced by Tracy and Widom. The essential step is to
recast the latter as isomonodromic deformation equations for families of
rational covariant derivative operators on the Riemann sphere and interpret
the Fredholm determinants as isomonodromic $\tau$-functions.