Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2002-02-18
Nonlinear Sciences
Exactly Solvable and Integrable Systems
57 pages
Scientific paper
The finite Pfaff lattice is given by commuting Lax pairs involving a finite matrix L (zero above the first subdiagonal) and a projection onto Sp(N). The lattice admits solutions such that the entries of the matrix L are rational in the time parameters t_1,t_2,..., after conjugation by a diagonal matrix. The sequence of polynomial tau-functions, solving the problem, belongs to an intriguing chain of subspaces of Schur polynomials, associated to Young diagrams, dual with respect to a finite chain of rectangles. Also, this sequence of tau-functions is given inductively by the action of a fixed vertex operator. As examples, one such sequence is given by Jack polynomials for rectangular Young diagrams, while another chain starts with any two-column Jack polynomial.
Adler Mark
Kuznetsov Vadim B.
Moerbeke Pierre van
No associations
LandOfFree
Rational solutions to the Pfaff lattice and Jack polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Rational solutions to the Pfaff lattice and Jack polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rational solutions to the Pfaff lattice and Jack polynomials will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-161916