Quantum integrability of the periodic Benjamin-Ono model
Maxim Nazarov (University of York)
Wednesday 22nd January, 2014 16:00-17:00 Maths 204
This is a joint work with Evgeny Sklyanin. A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions in those variables. It also provides a description of the stable non-negative spherical part of the trigonometric Cherednik algebra of type A.