A remark on Whittaker functions on SL ( n , ℝ )

Taku Ishii[1]

  • [1] Tokyo Institute of Technology, department of mathematics, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551 (JAPAN)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 2, page 483-492
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Ishii, Taku. "A remark on Whittaker functions on SL$(n,{\mathbb {R}})$." Annales de l’institut Fourier 55.2 (2005): 483-492. <http://eudml.org/doc/116197>.

@article{Ishii2005,
abstract = {We prove the recursive integral formula of class one $M$-Whittaker functions on SL$(n,\{\mathbb \{R\}\})$ conjectured and verified in case of $ n =3,4 $ by Stade.},
affiliation = {Tokyo Institute of Technology, department of mathematics, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551 (JAPAN)},
author = {Ishii, Taku},
journal = {Annales de l’institut Fourier},
keywords = {Whittaker functions; automorphic forms; Whittaker function; automorphic form},
language = {eng},
number = {2},
pages = {483-492},
publisher = {Association des Annales de l'Institut Fourier},
title = {A remark on Whittaker functions on SL$(n,\{\mathbb \{R\}\})$},
url = {http://eudml.org/doc/116197},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Ishii, Taku
TI - A remark on Whittaker functions on SL$(n,{\mathbb {R}})$
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 2
SP - 483
EP - 492
AB - We prove the recursive integral formula of class one $M$-Whittaker functions on SL$(n,{\mathbb {R}})$ conjectured and verified in case of $ n =3,4 $ by Stade.
LA - eng
KW - Whittaker functions; automorphic forms; Whittaker function; automorphic form
UR - http://eudml.org/doc/116197
ER -

References

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  1. W. N. Bailey, Generalized Hypergeometric Series, (1935) Zbl0011.02303
  2. D. Bump, Automorphic Forms on G L ( 3 , ℝ ) , Lect. Notes in Math. 1083 (1984) Zbl0543.22005MR765698
  3. M. Hashizume, Whittaker functions on semisimple Lie groups, Hiroshima Math. J. 12 (1982), 259-293 Zbl0524.43005MR665496
  4. H. Jacquet, Fonctions de Whittaker associées aux groupes de Chevalley, Bull. Soc. Math. France 95 (1967), 243-309 Zbl0155.05901MR271275
  5. B. Kostant, On Whittaker vectors and representation theory, Invent. Math. 48 (1978), 101-184 Zbl0405.22013MR507800
  6. R. Miatello, N. Wallach, Automorphic Forms Constructed from Whittaker Vectors, J. of Funct. Anal. 86 (1989), 411-487 Zbl0692.10029MR1021143
  7. J. Shalika, The multiplicity one theorem for G L ( n ) , Ann. of Math. 100 (1974), 171-193 Zbl0316.12010MR348047
  8. E. Stade, Poincaré Series For G L ( 3 , ℝ ) -Whittaker Functions, Duke Math. J. 3 (1989), 695-729 Zbl0699.10041MR1016442
  9. E. Stade, On Explicit Integral Formulas For G L ( n , ℝ ) -Whittaker Functions, Duke Math. J. 60 (1990), 313-362 Zbl0731.11027MR1047756
  10. E. Stade, G L ( 4 , ℝ ) -Whittaker functions and 4 F 3 ( 1 ) hypergeometric series, Trans. Amer. Math. Soc. 336 (1993), 253-264 Zbl0786.11027MR1102226
  11. E. Stade, The reciprocal of the beta function and G L ( n , ℝ ) Whittaker functions, Ann. Inst. Fourier, Grenoble 44 (1994), 93-108 Zbl0801.33001MR1262881

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