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Trace formula for coverings of connected reductive groups. I: Fine geometric expansion. (La formule des traces pour les revêtements de groupes réductifs connexes. I: Le développement géométrique fin.) (French) Zbl 1295.22027
This paper develops the geometric side of the Arthur-Selberg trace formula for the covering groups of connected reductive groups. The end result is an expansion in terms of weighted orbital integrals. The result is analogous to the case of connected reductive groups, with the main new ingredient being the notion of good orbits, where being good is a condition on the covering over the centralizer of a representative of the orbit.
The proof follows the arguments of Arthur, however this is by no means a simple extension of Arthur’s work. The author strives to prove a result in a general setting. The results are applicable to covering groups satisfying a set of precisely described conditions. In particular it is shown that the covering groups defined by the Brylinski-Deligne extension satisfy these conditions.
The paper contains a detailed discussion on the definition of covering groups. It can serve as a good reference.

MSC:
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
11F72 Spectral theory; trace formulas (e.g., that of Selberg)
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