Integrable structures arising from split symmetric pairs.
Jasper Stokman (University of Amsterdam)
Tuesday 13th March, 2018 16:00-17:00 Maths 311B
Harmonic analysis on symmetric spaces is known to be intimately related
to solving quantum Calogero-Moser systems. The reason is that the action of Casimirs on spherical
functions is described by the action of commuting differential operators on the radial components
of the spherical functions. In the first half of the talk I will extend this result to vector-valued
spherical functions. It leads to a new class of quantum spin Calogero-Moser systems.
In the second half of the talk I will attach boundary conformal blocks to
split symmetric pairs. I will show that they solve boundary versions of
Knizhnik-Zamolodchikov-Bernard type equations. These are compatible systems of
equations involving a new universal solution of the classical dynamical reflection
equation with respect to Felder's trigonometric dynamical r-matrix.
The first part of the talk naturally ties in because it provides compatible (higher) Laplace equations for
the boundary conformal blocks.
If time permits I will say something about the extension of the results to affine symmetric pairs.
The talk is based on joint work with Nicolai Reshetikhin.