Skip to main content Accessibility help

Eisenstein Series Arising from Jordan Algebras

  • Marcela Hanzer (a1) and Gordan Savin (a2)


We describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.



Hide All

Author M. H. was supported in part by a Croatian Science Foundation grant no. 9364. Author G. S. was supported in part by an NSF grant DMS-1359774.



Hide All
[1] Aubert, A.-M., Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif p-adique . Trans. Amer. Math. Soc. 347(1995), 21792189.
[2] Carter, R., Finite groups of Lie type: conjugacy classes and complex characters. Pure and Applied Mathematics, John Wiley & Sons, New York, 1985.
[3] Gan, W. T. and Savin, G., On minimal representations definitions and properties . Represent. Theory 9(2005), 4693.
[4] Gindikin, S. G. and Karpelevich, F. I., On an integral connected with symmetric Riemann spaces of nonpositive curvature. Translations. Series 2. American Mathematical Society, Providence, RI, 1969, pp. 249258.
[5] Goldfeld, D. and Hundley, J., Automorphic representations and L-functions for the general linear group. Volume I. Cambridge Studies in Advanced Mathematics, 129, Cambridge University Press, Cambridge, 2011.
[6] Hanzer, M., Unitarizability of a certain class of irreducible representations of classical groups . Manuscripta Math. 127(2008), 275307.
[7] Hanzer, M., The unitarizability of the Aubert dual of strongly positive square integrable representations . Israel J. Math. 169(2009), 251294.
[8] Hanzer, M., Non-Siegel Eisenstein series for symplectic groups . Manuscripta Math. 155(2018), 229302.
[9] Hanzer, M. and Muić, G., Degenerate Eisenstein series for Sp (4) . J. Number Theory 146(2015), 310342.
[10] Hanzer, M. and Muić, G., On the images and poles of degenerate Eisenstein series for  $\mathit{GL}(n,\mathbb{A})$  and  $\mathit{GL}(n,\mathbb{R})$ . Amer. J. Math. 137(2015), 907–951.
[11] Ikeda, T., On the theory of Jacobi forms and Fourier-Jacobi coefficients of Eisenstein series . J. Math. Kyoto Univ. 34(1994), 615636.
[12] Jacobson, N., Structure and representations of Jordan algebras. American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, RI, 1968.
[13] Kim, H. H., Exceptional modular form of weight 4 on an exceptional domain contained in C 27 . Rev. Mat. Iberoamericana 9(1993), 139200.
[14] Kobayashi, T. and Savin, G., Global uniqueness of small representations . Math. Z. 281(2015), 215239.
[15] Kudla, S. S. and Rallis, S., On the Weil-Siegel formula . J. Reine Angew. Math. 387(1988), 168.
[16] Kudla, S. S. and Rallis, S., A regularized Siegel-Weil formula: the first term identity . Ann. of Math. (2) 140(1994), 180.
[17] Langlands, R. P., Euler products. Yale Mathematical Monographs, 1, Yale University Press, New Haven, Conn.-London, 1971.
[18] Mœglin, C., Sur certains paquets d’Arthur et involution d’Aubert-Schneider-Stuhler généralisée . Represent. Theory 10(2006), 86129.
[19] Mœglin, C., Vignéras, M.-F., and Waldspurger, J.-L., Correspondances de Howe sur un corps p-adique. Lecture Notes in Mathematics, 1291, Springer-Verlag, Berlin, 1987.
[20] Sahi, S., Unitary representations on the Shilov boundary of a symmetric tube domain . In: Representation theory of groups and algebras, Contemp. Math., 145, American Mathematical Society, Providence, RI, 1993, pp. 275286.
[21] Sahi, S., Jordan algebras and degenerate principal series . J. Reine Angew. Math. 462(1995), 118.
[22] Weil, A., Sur certains groupes d’opérateurs unitaires . Acta Math. 111(1964), 143211.
[23] Weissman, M. H., The Fourier-Jacobi map and small representations . Represent. Theory 7(2003), 275299.
[24] Yamana, S., On the Siegel-Weil formula for quaternionic unitary groups . Amer. J. Math. 135(2013), 13831432.
MathJax is a JavaScript display engine for mathematics. For more information see


MSC classification

Eisenstein Series Arising from Jordan Algebras

  • Marcela Hanzer (a1) and Gordan Savin (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed