The negative symmetry flows are incorporated into the Riemann-Hilbert problem for the homogeneous Am-hierarchy and its gl̂(m+1, C) extension. A loop group automorphism of order two is used to define a sub-hierarchy of gl̂(m+1, C) hierarchy containing only the odd symmetry flows. The positive and negative flows of the ±1 grade coincide with equations of the multidimensional Toda model and of topological-anti-topological fusion.
Journal of Geometry and Physics
- Pub Date:
- April 2003
- High Energy Physics - Theory;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- 24+1 pages, some minus signs corrected