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Unitary dual of $p$-adic $GL\left( n \right)$. Proof of Bernstein conjectures


Author: Marko Tadić
Journal: Bull. Amer. Math. Soc. 13 (1985), 39-42
MSC (1980): Primary 22E50
MathSciNet review: 788387
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  • 1. Joseph N. Bernstein, 𝑃-invariant distributions on 𝐺𝐿(𝑁) and the classification of unitary representations of 𝐺𝐿(𝑁) (non-Archimedean case), Lie group representations, II (College Park, Md., 1982/1983) Lecture Notes in Math., vol. 1041, Springer, Berlin, 1984, pp. 50–102. MR 748505, 10.1007/BFb0073145
  • 2. Hervé Jacquet, On the residual spectrum of 𝐺𝐿(𝑛), Lie group representations, II (College Park, Md., 1982/1983) Lecture Notes in Math., vol. 1041, Springer, Berlin, 1984, pp. 185–208. MR 748508, 10.1007/BFb0073148
  • 3. François Rodier, Représentations de 𝐺𝐿(𝑛,𝑘) où 𝑘 est un corps 𝑝-adique, Bourbaki Seminar, Vol. 1981/1982, Astérisque, vol. 92, Soc. Math. France, Paris, 1982, pp. 201–218 (French). MR 689531
  • 4. Jonathan D. Rogawski, Representations of 𝐺𝐿(𝑛) and division algebras over a 𝑝-adic field, Duke Math. J. 50 (1983), no. 1, 161–196. MR 700135
  • 5. M. Tadić, The topology of the dual space of a reductive group over a local field, Glas. Mat. Ser. III 18(38) (1983), no. 2, 259–279 (English, with Serbo-Croatian summary). MR 733166
  • 6. M. Tadić, On the classification of irreducible unitary representations of GL (n) and the conjectures of Bernstein and Zelevinsky, Ann. Sci. École Norm. Sup. (to appear).
  • 7. Marko Tadić, Proof of a conjecture of Bernstein, Math. Ann. 272 (1985), no. 1, 11–16. MR 794086, 10.1007/BF01455923
  • 8. A. V. Zelevinsky, Induced representations of reductive 𝔭-adic groups. II. On irreducible representations of 𝔊𝔏(𝔫), Ann. Sci. École Norm. Sup. (4) 13 (1980), no. 2, 165–210. MR 584084

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DOI: https://doi.org/10.1090/S0273-0979-1985-15355-8