Pfaff
$\tau$-functions |
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| Authors: | M Adler T Shiota P van Moerbeke |
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| Institution: | (1) Department of Mathematics, Brandeis University, Waltham, MA 02454–9110, USA (e-mail: adler@math.brandeis.edu) , US;(2) Department of Mathematics, Kyoto University, Kyoto 606–8502, Japan (e-mail: shiota@kusm.kyoto-u.ac.jp) , JP;(3) Department of Mathematics, Université de Louvain, 1348 Louvain-la-Neuve, Belgium (e-mail: vanmoerbeke@geom.ucl.ac.be and @math.brandeis.edu) , BE |
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| Abstract: | Consider the two-dimensional Toda lattice, with certain skew-symmetric initial condition, which is preserved along the locus
of the space of time variables. Restricting the solution to , we obtain another hierarchy called Pfaff lattice, which has its own tau function, being equal to the square root of the
restriction of 2D-Toda tau function. We study its bilinear and Fay identities, W and Virasoro symmetries, relation to symmetric and symplectic matrix integrals and quasiperiodic solutions.
Received: 20 September 1999 / Published online: 1 February 2002 |
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| Keywords: | |
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