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Syracuse University

1991

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The Solution Space Of The Unitary Matrix Model String Equation And The Sato Grassmannian, Konstantinos N. Anagnostopoulos, Mark Bowick, Albert Schwarz Jan 1991

The Solution Space Of The Unitary Matrix Model String Equation And The Sato Grassmannian, Konstantinos N. Anagnostopoulos, Mark Bowick, Albert Schwarz

Physics

The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P; Q \Gamma ] = 1, with P and Q \Gamma 2 \Theta 2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations whose analysis ...