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Rational solutions to the Pfaff lattice and Jack polynomials | | Mark Adler
; Vadim B. Kuznetsov
; Pierre van Moerbeke
; | | Date: |
18 Feb 2002 | | Subject: | Exactly Solvable and Integrable Systems; Combinatorics; Mathematical Physics; Quantum Algebra; Classical Analysis and ODEs | nlin.SI hep-th math-ph math.CA math.CO math.MP math.QA | | Abstract: | 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. | | Source: | arXiv, nlin.SI/0202037 | | Services: | Forum | Review | PDF | Favorites | |
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