| eBook ISBN: | 978-1-4704-0244-0 |
| Product Code: | MEMO/137/655.E |
| List Price: | $50.00 |
| MAA Member Price: | $45.00 |
| AMS Member Price: | $30.00 |
| eBook ISBN: | 978-1-4704-0244-0 |
| Product Code: | MEMO/137/655.E |
| List Price: | $50.00 |
| MAA Member Price: | $45.00 |
| AMS Member Price: | $30.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 137; 1999; 112 ppMSC: Primary 11
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.
ReadershipGraduate 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.
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Table of Contents
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Chapters
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Introduction
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I. Preparations
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II. Main comparison
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III. Semi simple reduction
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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.
-
Chapters
-
Introduction
-
I. Preparations
-
II. Main comparison
-
III. Semi simple reduction
