PreprintGelfandKirillov conjecture and HarishChandra modules for finite WalgebrasV. Futorny, A. Molev and S. OvsienkoAbstractWe address two problems regarding the structure and representation theory of finite Walgebras associated with the general linear Lie algebras. Finite Walgebras can be defined either via the Whittaker modules of Kostant or, equivalently, by the quantum Hamiltonian reduction. Our first main result is a proof of the GelfandKirillov conjecture for the skew fields of fractions of the finite Walgebras. The second main result is a parametrization of finite families of irreducible HarishChandra modules by the characters of the GelfandTsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible HarishChandra modules for the finite Walgebras. This paper is available as a pdf (308kB) file.
