Matrix Integrals, Toda Symmetries, Virasoro Constraints and Orthogonal Polynomials Dédié Avec Admiration Au Professeur Paul Malliavin
نویسندگان
چکیده
into the algebras of skew-symmetric As and lower triangular (including the diagonal) matrices Ab (Borel matrices). We show that this splitting plays a prominent role also in the construction of the Toda symmetries and their action on τ−functions; it also plays a crucial role in obtaining the Virasoro constraints for matrix integrals and it ties up elegantly with the theory of orthogonal polynomials .
منابع مشابه
Symmetric random matrices and the Pfaff lattice
0. Introduction 1. Borel decomposition and the 2-Toda lattice 2. Two-Toda τ -functions and Pfaffian τ̃ -functions 3. The Pfaffian Toda lattice and skew-orthogonal polynomials 4. The (s = −t)-reduction of the Virasoro vector fields 5. A representation of the Pfaffian τ̃ -function as a symmetric matrix integral 6. String equations and Virasoro constraints 7. Virasoro constraints with boundary terms...
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