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.

Soit F un corps local non-archimédien. Dans cet article, nous commençons par décrire toutes les représentations irréductibles sphériques de GL(n,F). 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 GL(n,F) paraboliquement induite par une représentation unitaire irréductible, et la construction de Olshansky des séries complémentaires donnent directement le dual unitaire sphérique de GL(n,F).

Let F be a local non-archimedean field. The set of all equivalence classes of irreducible spherical representations of GL(n,F) 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 GL(n,F) 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 GL(n,F).

     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},
     zbl = {0554.20009},
     mrnumber = {87m:22047},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1046/}
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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://www.numdam.org/articles/10.5802/aif.1046/

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