The invariant trace formula. II: Global theory. (English) Zbl 0667.10019

Arthur, James

J. Am. Math. Soc. 1, No. 3, 501-554 (1988).

[For part I, cf. ibid., No.2, 323-383 (1988)]
This paper is one in the author’s monumental series on the Selberg trace formula for arbitrary reductive groups. In it the ‘spectral’ and ‘geometric’ sides of the invariant form of the trace formula are analyzed further into elementary distributions. These are rather difficult to define in general and remain still somewhat inaccessible. Nevertheless they can be computed in many simplified cases in which the Selberg trace formula becomes a very effective tool. The crucial fact proved in this paper is that all the distributions appearing in the Selberg trace formula are supported on characters which is proved by a long and subtle induction argument.

Reviewer: S.J.Patterson

MSC:

11F70	Representation-theoretic methods; automorphic representations over local and global fields
22E55	Representations of Lie and linear algebraic groups over global fields and adèle rings

Keywords:

invariant trace formula; global vanishing properties; invariant distributions; Selberg trace formula; reductive groups

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