\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Constructing automorphic representations in split classical groups

Abstract Related Papers Cited by
  • 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.
    Mathematics Subject Classification: Primary: 11F70.

    Citation:

    \begin{equation} \\ \end{equation}
  • [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. JiangSome conjectures on endoscopic representations in odd orthogonal groups, Nagoya Mathematical Journal, submitted.

    [10]

    D. Ginzburg, D. Jiang and D. SoudryOn 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.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(76) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return