Representations of algebraic groups over a 2-dimensional local field

Details Representations of algebraic groups over a 2-dimensional local field Representations of algebraic groups over a 2-dimensional local field

2003-02-14

arxiv.org/abs/math/0302174v5

Mathematics

Representation Theory

Revised version

Scientific paper

We introduce a categorical framework for the study of representations of $G_F$, where $G$ is a reductive group, and $\bF$ is a 2-dimensional local field, i.e. $F=K((t))$, where $K$ is a local field. Our main result says that the space of functions on $G_F$, which is an object of a suitable category of representations of $G_F$ with the respect to the action of $G_F$ on itself by left translations, becomes a representation of a certain central extension of $G_F$, when we consider the action by right translations.

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