Spectral curves, opers and integrable systems
-bundles and integrable hierarchies
We study the geometry of -bundles—locally projective -modules—on algebraic curves, and apply them to the study of integrable hierarchies, specifically the multicomponent Kadomtsev–Petviashvili (KP) and spin Calogero–Moser (CM) hierarchies. We show that KP hierarchies have a geometric description as flows on moduli spaces of -bundles; in particular, we prove that the local structure of -bundles is captured by the full Sato Grassmannian. The rational, trigonometric, and elliptic solutions of KP...
Page 1