Matching of Orbital Integrals on GL(4) and GSp(2) (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Flicker, Yuval Z.

Softcover

ISBN 10: 0821809598 ISBN 13: 9780821809594

Publisher: American Mathematical Society, 1999

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1999
• ISBN 10: 0821809598
• ISBN 13: 9780821809594
• Binding: Paperback
• Language: English
• Number of pages: 137