# Matching of Orbital Integrals on Gl(4) and GSP(2)

ISBN-10: 0821809598

ISBN-13: 9780821809594

Pub. Date: 01/04/1999

Publisher: American Mathematical Society

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

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## Overview

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.

## Product Details

ISBN-13:
9780821809594
Publisher:
American Mathematical Society
Publication date:
01/04/1999
Series:
Memoirs of the American Mathematical Society Series, #137
Pages:
112

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