### Abstract

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[Figure not available: see fulltext.] matrices of differential operators. These conditions on V_{1} and V_{2} yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints L_{n} (n≧0), where L_{n} annihilate the two modified-KdV τ-functions whose product gives the partition function of the Unitary Matrix Model.

Original language | English (US) |
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Pages (from-to) | 469-485 |

Number of pages | 17 |

Journal | Communications in Mathematical Physics |

Volume | 148 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1992 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Communications in Mathematical Physics*,

*148*(3), 469-485. https://doi.org/10.1007/BF02096545