Title: Integrable systems from the classical reflection equation
Speaker: Gus Schrader (University of California, Berkeley)
Abstract: The phase spaces of many well-known classical integrable systems, such as the relativistic Toda system and the classical periodic XXZ spin chain, can be realized as symplectic leaves of a quasitriangular Poisson-Lie group G. The Hamiltonians of such models are given by the restriction of conjugation-invariant functions on G. In a recent work, we construct integrable systems on Poisson homogeneous spaces of the form G/K, where the subgroup K arises as the fixed points of a group automorphism σ satisfying the classical reflection equation. We show that the subalgebra of K-bi-invariant functions on G is Poisson commutative, and that the Hamiltonian dynamics generated by these Hamiltonians are described by Lax equations. We will also explain how to realize the classical XXZ chain with reflecting boundaries as an example of our construction.