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

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

2004-06-14

arxiv.org/abs/math/0406282v4

Mathematics

Representation Theory

Scientific paper

In math.RT/0302174 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 $K$.

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