The Pfaff lattice and skew-orthogonal polynomials

@article{Adler1999ThePL,
  title={The Pfaff lattice and skew-orthogonal polynomials},
  author={Mark Adler and Emil Horozov and Pierre van Moerbeke},
  journal={International Mathematics Research Notices},
  year={1999},
  volume={1999},
  pages={569-588}
}
Consider a semi-inflnite skew-symmetric moment matrix, m1 evolving according to the vector flelds @m=@tk = ⁄ k m + m⁄ >k ; where ⁄ is the shift matrix. Then The skew-Borel decomposition m1 := Q i1 JQ >i1 leads to the so-called Pfafi Lattice, which is integrable, by virtue of the AKS theorem, for a splitting involving the a‐ne symplectic algebra. The tau-functions for the system are shown to be pfa‐ans and the wave vectors skew-orthogonal polynomials; we give their explicit form in terms of… 
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