Integrable Hierarchy for Multidimensional Toda Equations and Topological-Anti-topological Fusion

Physics – High Energy Physics – High Energy Physics - Theory

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24+1 pages, some minus signs corrected

Scientific paper

The negative symmetry flows are incorporated into the Riemann-Hilbert problem for the homogeneous $A_m$-hierarchy and its $\hat{gl} (m+1, C)$ extension. A loop group automorphism of order two is used to define a sub-hierarchy of $\hat{gl} (m+1, C)$ hierarchy containing only the odd symmetry flows. The positive and negative flows of the $\pm 1$ grade coincide with equations of the multidimensional Toda model and of topological-anti-topological fusion.

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