Multiplicity one for the Gelfand-Graev representation of a linear group

Dinakar Ramakrishnan

Compositio Mathematica (1982)

  • Volume: 45, Issue: 1, page 3-14
  • ISSN: 0010-437X

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Ramakrishnan, Dinakar. "Multiplicity one for the Gelfand-Graev representation of a linear group." Compositio Mathematica 45.1 (1982): 3-14. <http://eudml.org/doc/89509>.

@article{Ramakrishnan1982,
author = {Ramakrishnan, Dinakar},
journal = {Compositio Mathematica},
keywords = {linear group; Gel'fand-Graev representation; multiplicity; local field; connected reductive quasi-split group},
language = {eng},
number = {1},
pages = {3-14},
publisher = {Martinus Nijhoff Publishers},
title = {Multiplicity one for the Gelfand-Graev representation of a linear group},
url = {http://eudml.org/doc/89509},
volume = {45},
year = {1982},
}

TY - JOUR
AU - Ramakrishnan, Dinakar
TI - Multiplicity one for the Gelfand-Graev representation of a linear group
JO - Compositio Mathematica
PY - 1982
PB - Martinus Nijhoff Publishers
VL - 45
IS - 1
SP - 3
EP - 14
LA - eng
KW - linear group; Gel'fand-Graev representation; multiplicity; local field; connected reductive quasi-split group
UR - http://eudml.org/doc/89509
ER -

References

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  1. [1] I.N. Bernshtein and A.V. Zelevinsky: Representations of the group GL(n, F) where F is a non-archimedean local field. Russian Math. Surveys31, No. 3 (1976) 1-68. Zbl0348.43007
  2. [2] B. Blackadar: Thesis. University of California, Berkeley (1975). 
  3. [3] J. Dixmier: C*-algebras. North Holland Publishing Co. (1977). Zbl0372.46058MR458185
  4. [4] J. Dixmier and P. Malliavin: Factorisations de fonctions et de vecteurs differentiables. Bull. Soc. Math. France, 102, No. 4 (1978). Zbl0392.43013MR517765
  5. [5] I.M. Gelfand and M.I. Graev: Construction of irreducible representations of simple algebraic groups over finite fields. Soviet Math. Doklady, 3 (1962) 1642-1649. Zbl0119.26902
  6. [6] I.M. Gelfand and D.A. Kajdan: Representation of GL(n, K) where K is a local field, in Lie Groups and Representations, I.M. Gelfand, Ed., Halstead Press (1971) 95-118. Zbl0348.22011
  7. [7] A. Grothendieck: Produits tensoriels topologiques et espaces nucleaires. Mem. Am. Math. Soc., 16 (1955). Zbl0123.30301MR75539
  8. [8] H. Jacquet: Generic representations. Non-commutative Harmonic Analysis, Marseille-Luminy (1976). Zbl0357.22010MR499005
  9. [9] H. Jacquet and R.P. Langlands: Automorphic Forms on GL(2), Springer Lecture Notes, 114 (1970). Zbl0236.12010MR401654
  10. [10] B. Kostant: On Whittaker vectors and representation theory. Inventiones Mathematicae, 48 (1978) 101-184. Zbl0405.22013MR507800
  11. [11] G. Mackey: The Theory of Unitary Group Representations. University of Chicago Press, Chicago (1976). Zbl0344.22002MR396826
  12. [12] K. Maurin: Unitary Representations of Topological Groups. Polish Scientific Publishers, Warszawa (1968). Zbl0185.39001MR247377
  13. [13] Pjateckii-Shapiro: Euler Subgroups, in Lie Groups and Representations. I.M. Gelfand, Ed., Halstead Press (1971) 597-620. Zbl0329.20028MR406935
  14. [14] Pjateckii-Shapiro: Multiplicity One Theorems. Automorphic Forms, Representations and L-functions. A. Borel and W. Casselman, Eds., Proc. Symp. Pure Math., A.M.S., 33 (1979). Zbl0423.22017MR546599
  15. [15] A. Pietsch: Nukleare localkonvexe räume, Berlin (1965). Zbl0152.32302
  16. [16] D. Ramakrishnan: The Gelfand-Graev representation of GL(n) over a local field. Thesis, Columbia University (1980). 
  17. [17] F. Rodier: Whittaker models for admissible representations, Harmonic Analysis on Homogeneous Spaces, Symp. Pure Math., A.M.S., 26 (1972). Zbl0287.22016
  18. [18] J.A. Shalika: Multiplicity one theorem for GL(n). Annals of Math., 100, No. 1 (1974) 171-193. Zbl0316.12010MR348047

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