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Level One Algebraic Cusp Forms of Classical Groups of Small Rank. (Record no. 124849)

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000 -LEADER
fixed length control field 06074nam a22004813i 4500
001 - CONTROL NUMBER
control field EBC4832028
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240729131156.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s2015 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781470425098
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9781470410940
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC4832028
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL4832028
035 ## - SYSTEM CONTROL NUMBER
System control number (CaPaEBR)ebr11367313
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)917876223
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA243.C446 2016
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.7/4
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Chenevier, Gaëtan.
245 10 - TITLE STATEMENT
Title Level One Algebraic Cusp Forms of Classical Groups of Small Rank.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Providence :
Name of producer, publisher, distributor, manufacturer American Mathematical Society,
Date of production, publication, distribution, manufacture, or copyright notice 2015.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2015.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (134 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Memoirs of the American Mathematical Society ;
Volume/sequential designation v.237
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Title page -- Chapter 1. Introduction -- 1.1. A counting problem -- 1.2. Motivations -- 1.3. The main result -- 1.4. Langlands-Sato-Tate groups -- 1.5. The symplectic-orthogonal alternative -- 1.6. Case-by-case description, examples in low motivic weight -- 1.7. Generalizations -- 1.8. Methods and proofs -- 1.9. Application to Borcherds even lattices of rank 25 and determinant 2 -- 1.10. A level 1, non-cuspidal, tempered automorphic representation of \GL₂₈ over \Q with weights 0,1,2,\cdots,27 -- Chapter 2. Polynomial invariants of finite subgroups of compact connected Lie groups -- 2.1. The setting -- 2.2. The degenerate Weyl character formula -- 2.3. A computer program -- 2.4. Some numerical applications -- 2.5. Reliability -- 2.6. A check: the harmonic polynomial invariants of a Weyl group -- Chapter 3. Automorphic representations of classical groups : review of Arthur's results -- 3.1. Classical semisimple groups over \Z -- 3.2. Discrete automorphic representations -- 3.3. The case of Chevalley and definite semisimple \Z-groups -- 3.4. Langlands parameterization of Π_{ }( ) -- 3.5. Arthur's symplectic-orthogonal alternative -- 3.6. The symplectic-orthogonal alternative for polarized algebraic regular cuspidal automorphic representations of \GL_{ } over \Q -- 3.7. Arthur's classification: global parameters -- 3.8. The packet Π( ) of a ∈Ψ_{ }( ) -- 3.9. The character _{ } of _{ } -- 3.10. Arthur's multiplicity formula -- Chapter 4. Determination of Π_{ }^{⊥}(\PGL_{ }) for ≤5 -- 4.1. Determination of Π^{⊥}_{ }(\PGL₂) -- 4.2. Determination of Π_{ }^{ }(\PGL₄) -- 4.3. An elementary lifting result for isogenies -- 4.4. Symmetric square functoriality and Π^{⊥}_{ }(\PGL₃) -- 4.5. Tensor product functoriality and Π_{ }^{ }(\PGL₄) -- 4.6. Λ* functorality and Π_{ }^{ }(\PGL₅).
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note Chapter 5. Description of Π_{ }( ₇) and Π_{ }^{ }(\PGL₆) -- 5.1. The semisimple \Z-group ₇ -- 5.2. Parameterization by the infinitesimal character -- 5.3. Endoscopic partition of Π_{ }( ₇) -- 5.4. Conclusions -- Chapter 6. Description of Π_{ }( ₉) and Π_{ }^{ }(\PGL₈) -- 6.1. The semisimple \Z-group ₉ -- 6.2. Endoscopic partition of Π_{ } -- 6.3. Conclusions -- Chapter 7. Description of Π_{ }( ₈) and Π_{ }^{ }(\PGL₈) -- 7.1. The semisimple \Z-group ₈ -- 7.2. Endoscopic partition of Π_{ } -- 7.3. Conclusions -- Chapter 8. Description of Π_{ }( ₂) -- 8.1. The semisimple definite ₂ over \Z -- 8.2. Polynomial invariants for ₂(\Z)⊂ ₂(\R) -- 8.3. Endoscopic classification of Π_{ }( ₂) -- 8.4. Conclusions -- Chapter 9. Application to Siegel modular forms -- 9.1. Vector valued Siegel modular forms of level 1 -- 9.2. Two lemmas on holomorphic discrete series -- 9.3. An example: the case of genus 3 -- Appendix A. Adams-Johnson packets -- A.1. Strong inner forms of compact connected real Lie groups -- A.2. Adams-Johnson parameters -- A.3. Adams-Johnson packets -- A.4. Shelstad's parameterization map -- Appendix B. The Langlands group of \Z and Sato-Tate groups -- B.1. The locally compact group ℒ_{\Z} -- B.2. Sato-Tate groups -- B.3. A list in rank ≤8 -- Appendix C. Tables -- Appendix D. The 121 level 1 automorphic representations of ₂₅ with trivial coefficients -- Bibliography -- Back Cover.
520 ## - SUMMARY, ETC.
Summary, etc. The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of \mathrm{GL}_n over \mathbb Q of any given infinitesimal character, for essentially all n \leq 8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple \mathbb Z-forms of the compact groups \mathrm{SO}_7, \mathrm{SO}_8, \mathrm{SO}_9 (and {\mathrm G}_2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of \mathrm{GL}_n with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Forms (Mathematics).
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Renard, David A.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Chenevier, Gaëtan
Title Level One Algebraic Cusp Forms of Classical Groups of Small Rank
Place, publisher, and date of publication Providence : American Mathematical Society,c2015
International Standard Book Number 9781470410940
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Memoirs of the American Mathematical Society
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4832028">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4832028</a>
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