Irreducibility criteria for local and global representations
HTML articles powered by AMS MathViewer
- by Hiro-aki Narita, Ameya Pitale and Ralf Schmidt PDF
- Proc. Amer. Math. Soc. 141 (2013), 55-63 Request permission
Abstract:
It is proved that certain types of modular cusp forms generate irreducible automorphic representations of the underlying algebraic group. Analogous Archimedean and non-Archimedean local statements are also given.References
- Mahdi Asgari and Ralf Schmidt, Siegel modular forms and representations, Manuscripta Math. 104 (2001), no. 2, 173–200. MR 1821182, DOI 10.1007/PL00005869
- Rolf Berndt and Ralf Schmidt, Elements of the representation theory of the Jacobi group, Progress in Mathematics, vol. 163, Birkhäuser Verlag, Basel, 1998. MR 1634977, DOI 10.1007/978-3-0348-0283-3
- P. Cartier, Representations of $p$-adic groups: a survey, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 111–155. MR 546593
- Martin Eichler and Don Zagier, The theory of Jacobi forms, Progress in Mathematics, vol. 55, Birkhäuser Boston, Inc., Boston, MA, 1985. MR 781735, DOI 10.1007/978-1-4684-9162-3
- Stephen S. Gelbart, Automorphic forms on adèle groups, Annals of Mathematics Studies, No. 83, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. MR 0379375
- Ralf Schmidt, Iwahori-spherical representations of $\textrm {GSp}(4)$ and Siegel modular forms of degree 2 with square-free level, J. Math. Soc. Japan 57 (2005), no. 1, 259–293. MR 2114732
- Tamara B. Veenstra, Siegel modular forms, $L$-functions, and Satake parameters, J. Number Theory 87 (2001), no. 1, 15–30. MR 1816034, DOI 10.1006/jnth.2000.2586
- Hiroshi Yamashita, Multiplicity one theorems for generalized Gel′fand-Graev representations of semisimple Lie groups and Whittaker models for the discrete series, Representations of Lie groups, Kyoto, Hiroshima, 1986, Adv. Stud. Pure Math., vol. 14, Academic Press, Boston, MA, 1988, pp. 31–121. MR 1039835, DOI 10.2969/aspm/01410031
Additional Information
- Hiro-aki Narita
- Affiliation: Department of Mathematics, Kumamoto University, Kurokami, Kumamoto 860-8555, Japan
- Email: narita@sci.kumamoto-u.ac.jp
- Ameya Pitale
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
- MR Author ID: 778555
- Email: apitale@math.ou.edu
- Ralf Schmidt
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
- MR Author ID: 636524
- Email: rschmidt@math.ou.edu
- Received by editor(s): June 6, 2011
- Published electronically: May 1, 2012
- Additional Notes: The first author was partly supported by Grant-in-Aid for Young Scientists (B) 21740025, the Ministry of Education, Culture, Sports, Science and Technology, Japan
- Communicated by: Kathrin Bringmann
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 55-63
- MSC (2010): Primary 11F46, 11F50, 11F70; Secondary 22E50, 22E55
- DOI: https://doi.org/10.1090/S0002-9939-2012-11438-8
- MathSciNet review: 2988710