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Matching of Orbital Integrals on $GL(4)$ and $GSp(2)$
 
Yuval Z. Flicker Ohio State University, Columbus, OH
Front Cover for Matching of Orbital Integrals on GL(4) and GSp(2)
Available Formats:
Electronic 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
Front Cover for Matching of Orbital Integrals on GL(4) and GSp(2)
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  • Front Cover for Matching of Orbital Integrals on GL(4) and GSp(2)
  • Back Cover for Matching of Orbital Integrals on GL(4) and GSp(2)
Matching of Orbital Integrals on $GL(4)$ and $GSp(2)$
Yuval Z. Flicker Ohio State University, Columbus, OH
Available Formats:
Electronic 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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1371999; 112 pp
    MSC: 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.

    Readership

    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
     
     
    • Chapters
    • Introduction
    • I. Preparations
    • II. Main comparison
    • III. Semi simple reduction
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Volume: 1371999; 112 pp
MSC: 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.

Readership

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
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