Integrable Models and the Higher Dimensional Representations of Graded Lie Algebras

Details Integrable Models and the Higher Dimensional Representations of Graded Lie Algebras Integrable Models and the Higher Dimensional Representations of Graded Lie Algebras

1997-10-31

arxiv.org/abs/solv-int/9711001v1

Mod.Phys.Lett. A13 (1998) 133-144

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, latex

Scientific paper

10.1142/S0217732398000176

We construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling features of this model. This analysis, further, suggests a systematic method of constructing higher dimensional representations for the zero curvature condition starting with the fundamental representation. We illustrate this with the examples of the sTB hierarchy and the sKdV hierarchy. This would be particularly useful in constructing explicit higher dimensional representations of graded Lie algebras.

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