Matching of orbital integrals on and
About this Title
Yuval Z. Flicker
Publication: Memoirs of the American Mathematical Society
Publication Year 1999: Volume 137, Number 655
ISBNs: 978-0-8218-0959-4 (print); 978-1-4704-0244-0 (online)
MathSciNet review: 1468177
MSC (1991): Primary 11F70; Secondary 22E35, 22E50
The trace formula is the most powerful tool currently available to establish liftings of automorphic forms, as predicted by Langlands principle of functionality. The geometric part of the trace formula consists of orbital integrals, and the lifting is based on the fundamental lemma. The latter is an identity of the relevant orbital integrals for the unit elements of the Hecke algebras.
This volume concerns a proof of the fundamental lemma in the classically most interesting case of Siegel modular forms, namely the symplectic group $Sp(2)$. These orbital integrals are compared with those on $GL(4)$, twisted by the transpose inverse involution. The technique of proof is elementary. Compact elements are decomposed into their absolutely semi-simple and topologically unipotent parts also in the twisted case; a double coset decomposition of the form $H\backslash G/K$—where H is a subgroup containing the centralizer—plays a key role.
Graduate students and research mathematicians working in automorphic forms, trace formula, orbital integrals, conjugacy classes of rational elements in a classical group and in stable conjugacy.
Table of Contents
- I. Preparations
- II. Main comparison
- III. Semi simple reduction