Algebraic groups over a 2-dimensional local field: Some further constructions

Abstract

In [GK] we developed a framework to study representations of groups of the form G((t)), where G is an algebraic group over a local field K. The main feature of this theory is that natural representations of groups of this kind are not on vector spaces, but rather on pro-vector spaces. In this paper we present some further constructions related to this theory. The main results include: 1) General theorems insuring representability of covariant functors, 2) Study of the functor of semi-invariants, which is an analog of the functor of semi-infinite cohomology for infinite-dimensional Lie algebras, 3) Construction of representations from the moduli space of G-bundles on algebraic curve over K.