A remark on Whittaker functions on SL(n,ℝ)
[Une remarque sur les fonctions de Whittaker sur SL(n,ℝ)]
Ishii, Taku1
1 Tokyo Institute of Technology, department of mathematics, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551 (JAPAN)
Annales de l'Institut Fourier, Tome 55 (2005) no. 2, pp. 483-492.

Nous montrons des formules intégrales récursives pour les fonctions de M-Whittaker de classe un, qui ont été conjecturées (et vérifiées pour n=3,4) par Stade.

We prove the recursive integral formula of class one M-Whittaker functions on SL(n,ℝ) conjectured and verified in case of n=3,4 by Stade.

DOI : 10.5802/aif.2104
Classification : 11F55, 33C20
Keywords: Whittaker functions, automorphic forms
Mot clés : fonctions de Whittaker, formes automorphes
Ishii, Taku 1

1 Tokyo Institute of Technology, department of mathematics, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551 (JAPAN) 
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Ishii, Taku. A remark on Whittaker functions on SL$(n,{\mathbb {R}})$. Annales de l'Institut Fourier, Tome 55 (2005) no. 2, pp. 483-492. doi : 10.5802/aif.2104. http://www.numdam.org/articles/10.5802/aif.2104/

[1] W. N. Bailey Generalized Hypergeometric Series, Cambridge, 1935 | JFM | Zbl

[2] D. Bump Automorphic Forms on GL(3,ℝ), Lect. Notes in Math., Volume 1083 (1984) | MR | Zbl

[3] M. Hashizume Whittaker functions on semisimple Lie groups, Hiroshima Math. J., Volume 12 (1982), pp. 259-293 | MR | Zbl

[4] H. Jacquet Fonctions de Whittaker associées aux groupes de Chevalley, Bull. Soc. Math. France, Volume 95 (1967), pp. 243-309 | Numdam | MR | Zbl

[5] B. Kostant On Whittaker vectors and representation theory, Invent. Math., Volume 48 (1978), pp. 101-184 | DOI | MR | Zbl

[6] R. Miatello; N. Wallach Automorphic Forms Constructed from Whittaker Vectors, J. of Funct. Anal., Volume 86 (1989), pp. 411-487 | DOI | MR | Zbl

[7] J. Shalika The multiplicity one theorem for GL(n), Ann. of Math., Volume 100 (1974), pp. 171-193 | DOI | MR | Zbl

[8] E. Stade Poincaré Series For GL(3,ℝ)-Whittaker Functions, Duke Math. J., Volume 3 (1989), pp. 695-729 | MR | Zbl

[9] E. Stade On Explicit Integral Formulas For GL(n,ℝ)-Whittaker Functions, Duke Math. J., Volume 60 (1990) no. 2, pp. 313-362 | DOI | MR | Zbl

[10] E. Stade GL(4,ℝ)-Whittaker functions and 4 F 3 (1) hypergeometric series, Trans. Amer. Math. Soc., Volume 336 (1993) no. 1, pp. 253-264 | MR | Zbl

[11] E. Stade The reciprocal of the beta function and GL(n,ℝ) Whittaker functions, Ann. Inst. Fourier, Grenoble, Volume 44 (1994) no. 1, pp. 93-108 | DOI | Numdam | MR | Zbl

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