Abstract:

In this talk I would like to discuss my joint work with Susan Sierra about coadjoint orbits of Witt algebra (it is an algebraic version of Lie algebra of vector fields on a circle). I will start from general tools available for coadjoint representation of (infinite-dimensional) Lie algebras and then proceed to the case of the Witt Lie algebra. The final result for the Witt algebra is as follows: a) all coadjoint orbits with non-trivial closure are finite dimensional b) the elements of these orbits can be identified with linearly recurrent sequences of complex numbers c) the orbits themselves can be described through a version of n-jets of circle.