Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-13T06:52:03.410Z Has data issue: false hasContentIssue false
  • English
  • Français

Some conjectures on endoscopic representations in odd orthogonal groups

Published online by Cambridge University Press:  11 January 2016

David Ginzburg  and
Dihua Jiang
David Ginzburg
Affiliation:
School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Israel 69978, ginzburg@post.tau.ac.il
Dihua Jiang
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA, dhjiang@math.umn.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we introduce two conjectures on characterizations of endoscopy structures of irreducible generic cuspidal automorphic representations of odd special orthogonal groups in terms of nonvanishing of certain period of automorphic forms. We discuss a relation between the two conjectures and prove that a special case of Conjecture 1 (and hence Conjecture 2) is true.

Keywords

11F7022E55
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 208: Memorial Volume for Professor Hiroshi Saito , December 2012 , pp. 145 - 170
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2012

References

[A] Arthur, J., The endoscopic classification of representations: Orthogonal and symplectic groups, preprint, 2011.Google Scholar
[CKPS] Cogdell, J. W., Kim, H., Piatetski-Shapiro, I. I., and Shahidi, F., Functoriality for the classical groups, Publ. Math. Inst. Hautes Études Sci. 99 (2004), 163–233.CrossRefGoogle Scholar
[GS] Gan, W. T. and Savin, G., Real and global lifts from PGL3 to G2 , Int. Math. Res. Not. IMRN 50 (2003), 2699–2724.CrossRefGoogle Scholar
[G1] Ginzburg, D., A construction of CAP representations for classical groups, Int. Math. Res. Not. IMRN 20 (2003), 1123–1140.CrossRefGoogle Scholar
[G2] Ginzburg, D., Certain conjectures relating unipotent orbits to automorphic representations, Israel J. Math. 151 (2006), 323–355.CrossRefGoogle Scholar
[G3] Ginzburg, D., Endoscopic lifting in classical groups and poles of tensor L-functions, Duke Math. J. 141 (2008), 447–503.CrossRefGoogle Scholar
[GRS] Ginzburg, D., Rallis, S., and Soudry, D., The Descent Map from Automorphic Representations of GL(n) to Classical Groups, World Sci., Hackensack, N.J., 2011.Google Scholar
[Ich] Ichino, A., On the regularized Siegel-Weil formula, J. Reine Angew. Math. 539 (2001), 201–234.Google Scholar
[Ik] Ikeda, T., On the theory of Jacobi forms and Fourier-Jacobi coefficients of Eisenstein series, Kyoto J. Math. 34 (1994), 615–636.CrossRefGoogle Scholar
[J] Jiang, D., On the fundamental automorphic L-functions of SO(2n+1), Int. Math. Res. Not. IMRN 2006, Art. ID 64069.CrossRefGoogle Scholar
[JQ] Jiang, D. and Qin, Y.-J., Residues of Eisenstein series and generalized Shalika models for SO(4n), J. Ramanujan Math. Soc. 22 (2007), 101–133.Google Scholar
[JS] Jiang, D. and Soudry, D., On the genericity of cuspidal automorphic forms of SO2n+1, II, Compos. Math 143 (2007), 721–748.CrossRefGoogle Scholar
[KR] Kudla, S. S. and Rallis, S., A regularized Siegel-Weil formula: The first term identity, Ann. of Math. (2) 140 (1994), 1–80.CrossRefGoogle Scholar
[S] Soudry, D., Rankin-Selberg integrals, the descent method, and Langlands functoriality, Int. Congr. Math. 2, Eur. Math. Soc., Zürich, 2006, 1311–1325.Google Scholar