Periodic quantum integrable systems with deltainteractions and double affine Hecke algebras. 

Jasper V. Stokman, Kortewegde Vries Institute for Mathematics, University of Amsterdam, The Netherlands 

The
onedimensional quantum Bose gas with deltafunction interactions is a
particularly well studied integrable quantum manyparticle system. It
is directly linked to the integrable quantum field theory governed by
the nonlinear Schroedinger equation. In the present talk I aim to
clarify the parallels of such types of systems with onedimensional
integrable quantum manyparticle systems with long range interactions
(CalogeroMoser systems). Concretely, we discuss root system generalizations of quantum spinparticles on the circle with pairwise deltafunction interactions. We show that these quantum integrable systems naturally arise from a basic representation of a suitable degeneration of the double affine Hecke algebra in terms of vectorvalued Dunkltype operators. The associated Bethe ansatz equations and Bethe ansatz eigenfunctions are discussed in detail. This talk is based on joint work with Eric M. Opdam and Erdal Emsiz. 