On tensor third $L$-functions of automorphic representations of $\mathrm {GL}_n(\mathbb {A}_F)$
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Abstract:
Langlands’ beyond endoscopy proposal for establishing functoriality motivates interesting and concrete problems in the representation theory of algebraic groups. We study these problems in a setting related to the Langlands $L$-functions $L(s,\pi , \otimes ^3),$ where $\pi$ is a cuspidal automorphic representation of $\mathrm {GL}_n(\mathbb {A}_F)$ and $F$ is a global field.References
- James Arthur, The endoscopic classification of representations, American Mathematical Society Colloquium Publications, vol. 61, American Mathematical Society, Providence, RI, 2013. Orthogonal and symplectic groups. MR 3135650, DOI 10.1090/coll/061
- Dietrich Burde and Wolfgang Moens, Minimal faithful representations of reductive Lie algebras, Arch. Math. (Basel) 89 (2007), no. 6, 513–523. MR 2371687, DOI 10.1007/s00013-007-2378-x
- J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, Functoriality for the classical groups, Publ. Math. Inst. Hautes Études Sci. 99 (2004), 163–233. MR 2075885, DOI 10.1007/s10240-004-0020-z
- David Ginzburg, Stephen Rallis, and David Soudry, Generic automorphic forms on $\textrm {SO}(2n+1)$: functorial lift to $\textrm {GL}(2n)$, endoscopy, and base change, Internat. Math. Res. Notices 14 (2001), 729–764. MR 1846354, DOI 10.1155/S1073792801000381
- Robert Feger and Thomas W. Kephart, LieART—a Mathematica application for Lie algebras and representation theory, Comput. Phys. Commun. 192 (2015), 166–195. MR 3336706, DOI 10.1016/j.cpc.2014.12.023
- Igor Dolgachev, Lectures on invariant theory, London Mathematical Society Lecture Note Series, vol. 296, Cambridge University Press, Cambridge, 2003. MR 2004511, DOI 10.1017/CBO9780511615436
- William Fulton and Joe Harris, Representation theory, Graduate Texts in Mathematics, vol. 129, Springer-Verlag, New York, 1991. A first course; Readings in Mathematics. MR 1153249, DOI 10.1007/978-1-4612-0979-9
- Jayce R. Getz and Jamie Klassen, Isolating Rankin-Selberg lifts, Proc. Amer. Math. Soc. 143 (2015), no. 8, 3319–3329. MR 3348774, DOI 10.1090/proc/12389
- R. P. Langlands, Letter to André Weil (1967), http://publications.ias.edu/rpl/ section/21.
- Robert P. Langlands, Beyond endoscopy, Contributions to automorphic forms, geometry, and number theory, Johns Hopkins Univ. Press, Baltimore, MD, 2004, pp. 611–697. MR 2058622
- M. Larsen and R. Pink, Determining representations from invariant dimensions, Invent. Math. 102 (1990), no. 2, 377–398. MR 1074479, DOI 10.1007/BF01233432
- J. S. Milne, Algebraic Groups: An introduction to the theory of algebraic group schemes over fields, www.jmilne.org/math/.
- Richard P. Stanley, Enumerative combinatorics. Volume 1, 2nd ed., Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 2012. MR 2868112
Additional Information
- Heekyoung Hahn
- Affiliation: Department of Mathematics, Duke University, Durham, North Carolina 27708
- MR Author ID: 707443
- Email: hahn@math.duke.edu
- Received by editor(s): September 8, 2015
- Received by editor(s) in revised form: February 1, 2016
- Published electronically: May 4, 2016
- Communicated by: Ken Ono
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 5061-5069
- MSC (2010): Primary 11F70; Secondary 11F66, 11E57
- DOI: https://doi.org/10.1090/proc/13134
- MathSciNet review: 3556252