Representations of algebraic groups over a 2-dimensional local field

D. Gaitsgory; D. Kazhdan

paper

Representations of algebraic groups over a 2-dimensional local field

arXiv:math/0302174

Abstract

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.

Revised version