On Discrete Symmetries of the Multi-Boson KP Hierarchies

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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11 pgs, LaTeX, IFT-P/75/93, UICHEP-TH/93-17

Scientific paper

10.1016/0370-2693(94)90727-7

We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to the discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This establishes a canonical nature of the discrete transformations. The spectral equation, which defines both the lattice system and the corresponding Lax operator, plays a key role in determining pertinent symmetry structure. We also introduce a concept of the square-root lattice leading to a family of new pseudo-differential operators with covariance under additional B\"{a}cklund transformations.

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