| Description |
1 online resource (v, 122 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 237, number 1121 |
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Memoirs of the American Mathematical Society ; no. 1121.
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| Contents |
Chapter 1. Introduction Chapter 2. Polynomial invariants of finite subgroups of compact connected Lie groups Chapter 3. Automorphic representations of classical groups : review of Arthur's results Chapter 4. Determination of $\Pi _{\rm alg}̂\bot ({\rm PGL}_n)$ for $n\leq 5$ Chapter 5. Description of $\Pi _{\rm disc}({\rm SO}_7)$ and $\Pi _{\rm alg}̂{\rm s}({\rm PGL}_6)$ Chapter 6. Description of $\Pi _{\rm disc}({\rm SO}_9)$ and $\Pi _{\rm alg}̂{\rm s}({\rm PGL}_8)$ Chapter 7. Description of $\Pi _{\rm disc}({\rm SO}_8)$ and $\Pi _{\rm alg}̂{\rm o}({\rm PGL}_8)$ Chapter 8. Description of $\Pi _{\rm disc}({\rm G}_2)$ Chapter 9. Application to Siegel modular forms Appendix A. Adams-Johnson packets Appendix B. The Langlands group of $\mathbb {Z}$ and Sato-Tate groups Appendix C. Tables Appendix D. The $121$ level $1$ automorphic representations of ${\rm SO}_{25}$ with trivial coefficients |
| Summary |
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 o |
| Bibliography |
Includes bibliographical references (pages 117-122) |
| Notes |
"Volume 237, number 1121 (fifth of 6 numbers), September 2015." |
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Online resource; title from PDF title page (viewed October 6, 2015) |
| Subject |
Forms (Mathematics)
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Cusp forms (Mathematics)
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Cusp forms (Mathematics)
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Forms (Mathematics)
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| Form |
Electronic book
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| Author |
Renard, David, 1968- author.
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American Mathematical Society, publisher
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| ISBN |
9781470425098 |
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1470425092 |
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