Soit un corps local non-archimédien. Dans cet article, nous commençons par décrire toutes les représentations irréductibles sphériques de . En particulier, nous montrons que de telles représentations sont paraboliquement induites par des caractères non-ramifiés. Le résultat de Bernstein sur l’irréductibilité de la représentation de paraboliquement induite par une représentation unitaire irréductible, et la construction de Olshansky des séries complémentaires donnent directement le dual unitaire sphérique de .
Let be a local non-archimedean field. The set of all equivalence classes of irreducible spherical representations of is described in the first part of the paper. In particular, it is shown that each irreducible spherical representation is parabolically induced by an unramified character. Bernstein’s result on the irreducibility of the parabolically induced representations of by irreducible unitary ones, and Ol’shanskij’s construction of complementary series give directly a description of all equivalence classes of irreducible unitary spherical representations of .
@article{AIF_1986__36_2_47_0, author = {Tadic, Marko}, title = {Spherical unitary dual of general linear group over {non-Archimidean} local field}, journal = {Annales de l'Institut Fourier}, pages = {47--55}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {36}, number = {2}, year = {1986}, doi = {10.5802/aif.1046}, mrnumber = {87m:22047}, zbl = {0554.20009}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1046/} }
TY - JOUR AU - Tadic, Marko TI - Spherical unitary dual of general linear group over non-Archimidean local field JO - Annales de l'Institut Fourier PY - 1986 SP - 47 EP - 55 VL - 36 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.1046/ DO - 10.5802/aif.1046 LA - en ID - AIF_1986__36_2_47_0 ER -
%0 Journal Article %A Tadic, Marko %T Spherical unitary dual of general linear group over non-Archimidean local field %J Annales de l'Institut Fourier %D 1986 %P 47-55 %V 36 %N 2 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.1046/ %R 10.5802/aif.1046 %G en %F AIF_1986__36_2_47_0
Tadic, Marko. Spherical unitary dual of general linear group over non-Archimidean local field. Annales de l'Institut Fourier, Tome 36 (1986) no. 2, pp. 47-55. doi : 10.5802/aif.1046. http://archive.numdam.org/articles/10.5802/aif.1046/
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