On the spectral side of Arthur's trace formula --- combinatorial setup

Tobias Finis, Erez Lapid

Type: Article

Publication Date: 2011-06-22

Citations: 13

DOI: https://doi.org/10.4007/annals.2011.174.1.6

Abstract

In Arthur's trace formula, a ubiquitous role is played by certain limiting expressions arising from piecewise smooth functions with respect to projections of the Coxeter fan ((G, M )-families).These include terms resulting from intertwining operators on the spectral side and volumes of polytopes on the geometric side.We introduce the combinatorial concept of a compatible family with respect to an arbitrary polyhedral fan and obtain new formulas for the corresponding limiting expressions in this general framework.Our formulas can be regarded as algebraic generalizations of certain volume formulas for convex polytopes.In a companion paper, the results are used to study the spectral side of the trace formula.

Locations

Annals of Mathematics - View - PDF

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Works Cited by This (21)

Action	Title	Year	Authors
+	Polytopes and Brunn-Minkowski Theory	1994	Rolf Schneider
+	Introduction to Toric Varieties.	1993	William Fulton
+	Combinatorial Convexity and Algebraic Geometry	1996	Günter Ewald
+	The structure of the polytope algebra	1997	Michel Brion
+	Convex Bodies: The Brunn–Minkowski Theory	1993	Rolf Schneider
+	On a Family of Distributions Obtained from Eisenstein Series II: Explicit Formulas	1982	James Arthur
+	The algebra of continuous piecewise polynomials	1989	Louis J. Billera
+	The characters of discrete series as orbital integrals	1976	James Arthur
+	The Trace Formula in Invariant Form	1981	James Arthur
+	The spectral side of Arthur's trace formula	2009	Tobias Finis Erez Lapid Werner Müller