Constructing automorphic representations in split classicalgroups

David Ginzburg

doi:10.3934/era.2012.19.18

Article Contents

2012, Volume 19: 18-32. Doi: 10.3934/era.2012.19.18

This volume Previous Article Higher pentagram maps, weighted directed networks, and cluster dynamics Next Article On GIT quotients of Hilbert and Chow schemes of curves

Constructing automorphic representations in split classical groups

David Ginzburg^1,

1.
School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978

Received: May 31, 2011

Revised: November 30, 2011

Published: December 2011

Abstract Related Papers Cited by

Abstract

In this paper we introduce a general construction for a correspondence between certain Automorphic representations in classical groups. This construction is based on the method of small representations, which we use to construct examples of CAP representations.

Keywords:

Functorial lifting,
small representations.

Mathematics Subject Classification: Primary: 11F70.

Citation:

Related Papers

Cited by

References

[1]	R. Carter, "Finite Groups of Lie Type," J. Wiley & Sons, 1985.
[2]	J. Cogdell, H. Kim, I. Piatetski-Shapiro and F. Shahidi, Functoriality for the classical groups, 99 (2004), 163-233.
[3]	D. Collingwood and W. McGovern, "Nilpotent Orbits in Semisimple Lie Algebras," Van Nostrand Reinhold, 1991.
[4]	D. Ginzburg, "A construction of CAP representations for classical groups," International Math. Research Notices, 20 (2003), 1123-1140.doi: 10.1155/S1073792803212228.
[5]	D. Ginzburg, Certain conjectures relating unipotent orbits to automorphic representations, Israel Journal of Mathematics, 151 (2006), 323-356.doi: 10.1007/BF02777366.
[6]	D. Ginzburg, Endoscopic lifting in classical groups and poles of tensor $L$ functions, Duke Math. Journal, 141 (2008), 447-503.doi: 10.1215/00127094-2007-002.
[7]	D. Ginzburg, On the lifting from $PGL_2\times PGL_2$ to $G_2$, International Math. Research Notices, 25 (2005), 1499-1518.
[8]	D. Ginzburg and D. Jiang, Periods and liftings: From $G_2$ to $C_3$, Israel Journal of Math., 123 (2001), 29-59.doi: 10.1007/BF02784119.
[9]	D. Ginzburg and D. Jiang, Some conjectures on endoscopic representations in odd orthogonal groups, Nagoya Mathematical Journal, submitted.
[10]	D. Ginzburg, D. Jiang and D. Soudry, On CAP representations for even orthogonal groups I: A correspondence of unramified representations, preprint.
[11]	D. Ginzburg, D. Jiang and S. Rallis, On CAP automorphic representations of a split group of type $D_4$, J. Reine Angew. Math., 552 (2002), 179-211.doi: 10.1515/crll.2002.090.
[12]	D. Ginzburg, D. Jiang and S. Rallis, Periods of residual representations of $SO(2l)$, Manuscripta Mathematica, 113 (2004), 319-358.doi: 10.1007/s00229-003-0417-x.
[13]	D. Ginzburg, S. Rallis and D. Soudry, "The Descent Map from Automorphic Representations of $GL(n)$ to Classical Groups," World Scientific, 2011.doi: 10.1142/9789814304993.
[14]	D. Ginzburg, S. Rallis and D. Soudry, Construction of CAP representations for symplectic groups using the descent method, in "Automorphic Representations, $L$ Functions and Applications: Progress and Prospects," de-Gruyter, (2005), 193-224.
[15]	H. Jacquet, On the residual spectrum of $GL(n)$, in "Lie Group Representations," II (College Park, Md., 1982/1983), Lecture Notes in Math., 1041, Springer, Berlin, (1984), 185-208.
[16]	I. I. Piatetski-Shapiro, On the Saito-Kurokawa lifting, Invent. Math., 71 (1983), 309-338.doi: 10.1007/BF01389101.