Oleg Sheinman

Highest weight representations of Krichever-Novikov algebras and integrable systems

Affine Krichever-Novikov algebras appear as a natural generalization (related to any Riemann surface of a positive genus) of affine Kac-Moody algebras. No Cartan-Weyl-type theory is known for this class of Lie algebras. The talk is devoted to the recently found relationship between the highest weight representations of these algebras and certain completely integrable systems on the spaces of their coadjoint orbits.