The Pfaff lattice and skew-orthogonal polynomials
| dc.creator | Adler, M. | |
| dc.creator | Horozov, E. | |
| dc.creator | van Moerbeke, P. | |
| dc.date | 1999-03-04 | |
| dc.date | 1999-04-27 | |
| dc.date.accessioned | 2026-07-07T06:17:46Z | |
| dc.date.available | 2026-07-07T06:17:46Z | |
| dc.description | 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. Then the skew-Borel decomposition $ m_{\iy}:= Q^{-1} J Q^{\top -1} $ leads to the so-called Pfaff Lattice, which is integrable, by virtue of the AKS theorem, for a splitting involving the affine symplectic algebra. The tau-functions for the system are shown to be pfaffians and the wave vectors skew-orthogonal polynomials; we give their explicit form in terms of moments. This system plays an important role in symmetric and symplectic matrix models and in the theory of random matrices (beta=1 or 4). | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/solv-int/9903005 | |
| dc.identifier | http://arxiv.org/abs/solv-int/9903005 | |
| dc.identifier | Intern. Math. Research Notices, 1999 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94501 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | The Pfaff lattice and skew-orthogonal polynomials | |
| dc.type | text |