Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-27T22:05:37.645Z Has data issue: false hasContentIssue false
  • English
  • Français

Bruhat Order and Transfer for Complex Reductive Groups

Published online by Cambridge University Press:  20 November 2018

Martin Andler
Martin Andler*
Affiliation:
Département de mathématiques et informatique (UA 762 du CNRS), École normale supérieure, 45 rued'Ulm, 75230 Paris Cedex 05
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a complex reductive group, and G^ its set of irreducible admissible representations. The Bruhat order on G^ is defined in a natural way. We prove that this Bruhat order is preserved by transfer. This gives new proofs of some results by the author on L-functions.

Keywords

22 E11F
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 5 , 01 October 1992 , pp. 911 - 923
Copyright
Copyright © Canadian Mathematical Society 1992

References

[A-V] Adams, J. and Vogan, D., Lifting of characters and Harish Chandra's method of descent. Google Scholar
[A] Andler, M., Relationships of divisibility between local L-functions associated to representations of complex reductive groups. In: Non commutative harmonic analysis and Lie groups, Lecture Notes in Math. 1243, Springer, Heidelberg, (1987). 1-14.Google Scholar
[B-G] Bernstein, J. and Gelfand, I.M., Tensor product of finite and infinite dimensional representations of semisimple Lie algebras, Compositio Math.. 41(1980), 245–285.Google Scholar
[B] Borel, A., Automorphic L-functions. In: Automorphic forms, Representations and L-functions, Proceedings of Symposia in Pure Mathematics, part II, Amer. Math. Soc, Providence. 33(1979), 27–60.Google Scholar
[Bou] Bourbaki, N., Groupes et algèbres de Lie, Hermann, Paris, 1968.Google Scholar
[Dl] Duflo, M., Représentations irréductibles des groupes semi-simples complexes. In: Analyse harmonique sur les groupes de Lie, Lecture Notes in Math. 497, Springer, Heidelberg, (1975). 26-88.Google Scholar
[D2] Duflo, M., Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semisimple, Annals of Math. 105(1977), 107–120.Google Scholar
[G-J] Godement, R. and Jacquet, H., Zêtafunctions of simple Lie algebras, Lecture Notes in Math. 260, Springer, Heidelberg, 1972.Google Scholar
[H] Hirai, T., Structure of Induced Representations and Characters of Irreducible Representations of Complex Semi-Simple Lie Groups. In: Conference on Harmonic Analysis, Lecture Notes in Math. 266, Springer, Heidelberg, (1972). 167-188.Google Scholar
[J] Jacquet, H., Principal L-functions of the linear group. In: Automorphic forms, Representations and Lfunctions, Proceedings of Symposia in Pure Mathematics, part II, American Math. Society, Providence,. 33(1979), 63–86.Google Scholar
[J-L] Jacquet, H. and Langlands, R.P., Automorphic forms on GL(2), Lecture Notes in Math. 114, Springer, Heidelberg, 1970.Google Scholar
[L] Langlands, R.P., On the classification of irreducible representations of real reductive groups-1973. In: Representation theory and harmonic analysis on semi-simple Lie groups, Math, surveys and monographs, American Math. Society, Providence,. 31(1989), 101–170.Google Scholar
[VI] Vogan, D., Representations of Real Reductive Lie Groups, Birkhauser, Boston, 1981.Google Scholar
[V2] Vogan, D., Private communication, 1990.Google Scholar