Pfaff taufunctions
Abstract
Consider the evolution $$ \frac{\pl m_\iy}{\pl t_n}=\Lb^n m_\iy, \frac{\pl m_\iy}{\pl s_n}=m_\iy(\Lb^\top)^n, $$ on bi or semiinfinite matrices $m_\iy=m_\iy(t,s)$, with skewsymmetric initial data $m_{\iy}(0,0)$. Then, $m_\iy(t,t)$ is skewsymmetric, and so the determinants of the successive "upperleft corners" vanish or are squares of Pfaffians. In this paper, we investigate the rich nature of these Pfaffians, as functions of t. This problem is motivated by questions concerning the spectrum of symmetric and symplectic random matrix ensembles.
 Publication:

arXiv eprints
 Pub Date:
 September 1999
 arXiv:
 arXiv:solvint/9909010
 Bibcode:
 1999solv.int..9010A
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 High Energy Physics  Theory;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems
 EPrint:
 42 pages