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On tensor third $ L$-functions of automorphic representations of $ GL_n(\mathbb{A}_F)$


Author: Heekyoung Hahn
Journal: Proc. Amer. Math. Soc. 144 (2016), 5061-5069
MSC (2010): Primary 11F70; Secondary 11F66, 11E57
DOI: https://doi.org/10.1090/proc/13134
Published electronically: May 4, 2016
MathSciNet review: 3556252
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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 $ \textup {GL}_n(\mathbb{A}_F)$ and $ F$ is a global field.


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  • [A] James Arthur, The endoscopic classification of representations: Orthogonal and symplectic groups, American Mathematical Society Colloquium Publications, vol. 61, American Mathematical Society, Providence, RI, 2013. MR 3135650
  • [BM] Dietrich Burde and Wolfgang Moens, Minimal faithful representations of reductive Lie algebras, Arch. Math. (Basel) 89 (2007), no. 6, 513-523. MR 2371687, https://doi.org/10.1007/s00013-007-2378-x
  • [CKPSS] 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, https://doi.org/10.1007/s10240-004-0020-z
  • [GRS01] David Ginzburg, Stephen Rallis, and David Soudry, Generic automorphic forms on $ {\rm SO}(2n+1)$: functorial lift to $ {\rm GL}(2n)$, endoscopy, and base change, Internat. Math. Res. Notices 14 (2001), 729-764. MR 1846354, https://doi.org/10.1155/S1073792801000381
  • [FK] 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, https://doi.org/10.1016/j.cpc.2014.12.023
  • [Do] Igor Dolgachev, Lectures on invariant theory, London Mathematical Society Lecture Note Series, vol. 296, Cambridge University Press, Cambridge, 2003. MR 2004511
  • [FH] William Fulton and Joe Harris, Representation theory, A first course, Graduate Texts in Mathematics, vol. 129, Readings in Mathematics, Springer-Verlag, New York, 1991. MR 1153249
  • [GK] Jayce R. Getz and Jamie Klassen, Isolating Rankin-Selberg lifts, Proc. Amer. Math. Soc. 143 (2015), no. 8, 3319-3329. MR 3348774, https://doi.org/10.1090/proc/12389
  • [L1] R. P. Langlands, Letter to André Weil (1967), http://publications.ias.edu/rpl/
    section/21.
  • [L2] 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
  • [LP] M. Larsen and R. Pink, Determining representations from invariant dimensions, Invent. Math. 102 (1990), no. 2, 377-398. MR 1074479, https://doi.org/10.1007/BF01233432
  • [M] J. S. Milne, Algebraic Groups: An introduction to the theory of algebraic group schemes over fields, www.jmilne.org/math/.
  • [St] Richard P. Stanley, Enumerative combinatorics. Volume 1, 2nd ed., Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 2012. MR 2868112

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Additional Information

Heekyoung Hahn
Affiliation: Department of Mathematics, Duke University, Durham, North Carolina 27708
Email: hahn@math.duke.edu

DOI: https://doi.org/10.1090/proc/13134
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
Article copyright: © Copyright 2016 American Mathematical Society

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