A nonlinear deformation is conjectured for the reduction of the 3~(rd) 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 {(_(2s+1)~(2n+1))(4~(s+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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