Geodesic
Eisenstein Series Arising from Jordan Algebras
Canadian journal of mathematics, Tome 72 (2020) no. 1, pp. 183-201

Voir la notice de l'article provenant de la source Cambridge University Press

We describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.
DOI : 10.4153/CJM-2018-033-2
Mots-clés : Eisenstein series, Jordan algebra, Fourier-Jacobi functor 
Hanzer, Marcela; Savin, Gordan. Eisenstein Series Arising from Jordan Algebras. Canadian journal of mathematics, Tome 72 (2020) no. 1, pp. 183-201. doi: 10.4153/CJM-2018-033-2
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[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), 2179–2189. . Google Scholar | DOI

[2] Carter, R., Finite groups of Lie type: conjugacy classes and complex characters . Pure and Applied Mathematics, John Wiley & Sons, New York, 1985. Google Scholar

[3] Gan, W. T. and Savin, G., On minimal representations definitions and properties . Represent. Theory 9(2005), 46–93. . Google Scholar | DOI

[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. 249–258. . Google Scholar | DOI

[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. . Google Scholar | DOI

[6] Hanzer, M., Unitarizability of a certain class of irreducible representations of classical groups . Manuscripta Math. 127(2008), 275–307. . Google Scholar | DOI

[7] Hanzer, M., The unitarizability of the Aubert dual of strongly positive square integrable representations . Israel J. Math. 169(2009), 251–294. . Google Scholar | DOI

[8] Hanzer, M., Non-Siegel Eisenstein series for symplectic groups . Manuscripta Math. 155(2018), 229–302. . Google Scholar | DOI

[9] Hanzer, M. and Muić, G., Degenerate Eisenstein series for Sp (4) . J. Number Theory 146(2015), 310–342. . Google Scholar | DOI

[10] Hanzer, M. and Muić, G., On the images and poles of degenerate Eisenstein series for  and . Amer. J. Math. (2015), 907–951. . Google Scholar | DOI

[11] Ikeda, T., On the theory of Jacobi forms and Fourier-Jacobi coefficients of Eisenstein series . J. Math. Kyoto Univ. 34(1994), 615–636. . Google Scholar | DOI

[12] Jacobson, N., Structure and representations of Jordan algebras . American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, RI, 1968. Google Scholar

[13] Kim, H. H., Exceptional modular form of weight 4 on an exceptional domain contained in 27 . Rev. Mat. Iberoamericana 9(1993), 139–200. . Google Scholar | DOI

[14] Kobayashi, T. and Savin, G., Global uniqueness of small representations . Math. Z. 281(2015), 215–239. . Google Scholar | DOI

[15] Kudla, S. S. and Rallis, S., On the Weil-Siegel formula . J. Reine Angew. Math. 387(1988), 1–68. . Google Scholar | DOI

[16] Kudla, S. S. and Rallis, S., A regularized Siegel-Weil formula: the first term identity . Ann. of Math. (2) 140(1994), 1–80. . Google Scholar | DOI

[17] Langlands, R. P., Euler products . Yale Mathematical Monographs, 1, Yale University Press, New Haven, Conn.-London, 1971. Google Scholar

[18] Mœglin, C., Sur certains paquets d’Arthur et involution d’Aubert-Schneider-Stuhler généralisée . Represent. Theory 10(2006), 86–129. . Google Scholar | DOI

[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. . Google Scholar | DOI

[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. 275–286. . Google Scholar | DOI

[21] Sahi, S., Jordan algebras and degenerate principal series . J. Reine Angew. Math. 462(1995), 1–18. . Google Scholar | DOI

[22] Weil, A., Sur certains groupes d’opérateurs unitaires . Acta Math. 111(1964), 143–211. . Google Scholar | DOI

[23] Weissman, M. H., The Fourier-Jacobi map and small representations . Represent. Theory 7(2003), 275–299. . Google Scholar | DOI

[24] Yamana, S., On the Siegel-Weil formula for quaternionic unitary groups . Amer. J. Math. 135(2013), 1383–1432. . Google Scholar | DOI

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