FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 7, PAGES 101-116

On skew-symmetric and general deformations of Lax pseudodifferential operators

B. A. Kupershmidt

Abstract

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A nonlinear deformation is conjectured for the reduction of the third KP flow on the subspace of skew-symmetric operators, and the conjecture is proved for the linearized flow. As a by-product, we find a peculiar (nonquantum) polynomial deformation of the numbers $\{\; \backslash binom\{2n+1\}\{2s+1\}\; (4s+1-1)/(s+1)\; B$_2s+2 }, where $B$_m's are the Bernoulli numbers. General open questions and generalizations are also discussed. The conjecture is extended to all the flows, and its linearized version is proved.

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Last modified: February 13, 2007