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Geometric aspects of the trace formula

Author: Werner Müller; Sug Woo Shin; Nicolas Templier
Publisher: Cham, Switzerland : Springer, [2018] ©2018
Series: Simons symposia.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups. Based on research presented at the 2016 Simons Symposium on Geometric Aspects of the Trace Formula that took place in Schloss Elmau, Germany, the volume contains both original research articles and articles that synthesize current knowledge and future directions in the  Read more...
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Genre/Form: Electronic books
Additional Physical Format: (OCoLC)1038441132
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Werner Müller; Sug Woo Shin; Nicolas Templier
ISBN: 9783319948331 3319948334 9783319948348 3319948342 9783030069223 3030069222
OCLC Number: 1056952117
Language Note: Text in English with two papers in French.
Description: 1 online resource.
Contents: Intro; Preface; Introduction; Contents; Functoriality and the Trace Formula; Foreword; 1 The Principle of Functoriality; 2 The Trace Formula; 3 A Stratification; 4 Further Thoughts; References; Graded Hecke Algebras for Disconnected Reductive Groups; 1 Introduction; 2 The Relation with Langlands Parameters; 3 The Twisted Graded Hecke Algebra of a Cuspidal Support; 4 Representations of Twisted Graded Hecke Algebras; 4.1 Standard Modules; 4.2 Representations Annihilated by r; 4.3 Intertwining Operators and 2-Cocycles; 4.4 Parametrization of Irreducible Representations 4.5 Tempered Representations and the Discrete Series5 The Twisted Graded Hecke Algebra of a Cuspidal Quasi-Support; References; Sur une variante des troncatures d'Arthur; 1 Introduction; 2 Variations sur les constructions d'Arthur; 3 Une autre troncature; 4 Noyaux modifiés; 5 Intégrale orbitale tronquée; 6 Contributions des orbites et intégrales orbitales; 7 Intégrales tronquées de séries d'Eisenstein; 8 Intégrales zêta associées à une orbite nilpotente; 9 Calcul d'intégrales orbitales nilpotentes tronquées; 10 L'énoncé final; 11 Une conjecture; Références Twisted Endoscopy from a Sheaf-Theoretic Perspective1 Introduction; 2 Recollections from Adams-Barbasch-Vogan; 3 Automorphisms; 3.1 Characterizations of Automorphisms; 3.2 Actions on (G/R) and (G); 4 Twisting and the Local Langlands Correspondence; 4.1 The -Equivariance of the Local Langlands Correspondence for Tori; 4.2 The -Equivariance of the Local Langlands Correspondence for Reductive Groups; 5 Twisted Endoscopy; 5.1 Twisted Endoscopic Data; 5.2 Endoscopic Lifting; 5.3 Standard Endoscopic Lifting; 5.4 Twisted Endoscopic Lifting 6 Twisted Endoscopy for GLN and Arthur Packets of Classical GroupsReferences; The Subregular Unipotent Contribution to the Geometric Side of the Arthur Trace Formula for the Split Exceptional Group G2; 1 Introduction; 2 Main Result; 3 The Group of Type G2 and the Space of Binary Cubic Forms; 4 Proof of the Main Result; 5 Proofs of Two Lemmas; 5.1 Proof of Lemma 4.2; 5.2 Proof of Lemma 4.3; References; The Shimura-Waldspurger Correspondence for Mp(2n); 1 Introduction; 2 Automorphic Discrete Spectrum via Theta Correspondence; 2.1 Local Shimura Correspondence; 2.2 Global Results 2.3 The Tempered Part2.4 Multiplicity Formula; 2.5 Theta Lifting; 2.6 Results of J.S. Li; 2.7 Assignment of A-Parameters; 2.8 Proof of Proposition 2.7; 2.9 Equality?; 2.10 Key Proposition for Tempered; 2.11 Proof of Key Proposition; 2.12 Local Packets; 3 Endoscopy and Character Identities for Mp(2n); 3.1 Basic Formalism; 3.2 Endoscopy; 3.3 Review of Vogan Packets for SO(2n+1); 3.4 Desiderata for LLC of Mp(2n,k); 3.5 Case Study: n=1; 3.6 The Local Conjecture; 3.7 The Case of General n; 4 Stable Trace Formula and Local Intertwining Relations; 4.1 Automorphic Discrete Spectrum
Series Title: Simons symposia.
Responsibility: editors, Werner Müller, Sug Woo Shin and Nicolas Templier.

Abstract:

The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups. Based on research presented at the 2016 Simons Symposium on Geometric Aspects of the Trace Formula that took place in Schloss Elmau, Germany, the volume contains both original research articles and articles that synthesize current knowledge and future directions in the field. The articles discuss topics such as the classification problem of representations of reductive groups, the structure of Langlands and Arthur packets, interactions with geometric representation theory, and conjectures on the global automorphic spectrum. Suitable for both graduate students and researchers, this volume presents the latest research in the field. Readers of the first volume Families of Automorphic Forms and the Trace Formula will find this a natural continuation of the study of the trace formula.--

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