63 citations · 64 across the 3 of their papers we have counts for
4 papers · 1 filter
The Pfaff lattice, Matrix integrals and a map from Toda to Pfaff
M. Adler, P. van Moerbeke
We study the Pfaff lattice, introduced by us in the context of a Lie algebra splitting of gl(infinity) into sp(infinity) and lower-triangular matrices. We establish a set of biline…
The Pfaff lattice and skew-orthogonal polynomials
M. Adler, E. Horozov, P. van Moerbeke
Consider a semi-infinite skew-symmetric moment matrix, $m_{\iy}$ evolving according to the vector fields $\pl m / \pl t_k=\Lb^k m+m \Lb^{\top k} ,$ where $\Lb$ is the shift matrix.…
Random matrices, Virasoro algebras, and noncommutative KP
M. Adler, T. Shiota, P. van Moerbeke
What is the connection of random matrices with integrable systems? Is this connection really useful? The answer to these questions leads to a new and unifying approach to the theor…
Toda-Darboux maps and vertex operators
M. Adler, P. van Moerbeke
The purpose of this paper is to study Toda-Darboux transforms, i.e., Darboux transforms for operators L(t) flowing according to the Toda lattice. Each element of the null-space $L(…