Canonical bases, toric degenerations, and collective integrable systems
Canonical bases, toric degenerations, and collective integrable systems
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Passcode:听998749
There are three important settings for studying actions of reductive Lie groups: modules, algebraic group actions, and Hamiltonian group actions. In the study of modules one encounters various constructions of nice bases which are in some sense canonical (e.g. Gelfand-Zeitlin, Lusztig). 听In the study of algebraic group actions canonical bases give rise to toric degenerations; deformations of the G-variety to a toric variety (cf. Caldero, Alexeev-Brion).听
In this talk I will discuss the symplectic analogue of these constructions: integrable systems. We show how 听toric degenerations 听give rise to听integrable systems on arbitrary听symplectic manifolds equipped with Hamiltonian group actions. This generalizes a family of well-known examples called Gelfand-Zeitlin integrable systems due to Guillemin and Sternberg. 听As a by-product, we 听generalize results of Harada and Kaveh on construction integrable systems from toric degenerations.
This talk is based on joint work with Benjamin Hoffman.听