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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Some examples of square integrable representations of semisimple $p$-adic groups
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by George Lusztig PDF
Trans. Amer. Math. Soc. 277 (1983), 623-653 Request permission


We construct irreducible representations of the Hecke algebra of an affine Weyl group analogous to Kilmoyer’s reflection representation corresponding to finite Weyl groups, and we show that in many cases they correspond to a square integrable representation of a simple $p$-adic group.
  • I. N. BernÅ¡teÄ­n and A. V. ZelevinskiÄ­, Representations of the group $GL(n,F),$ where $F$ is a local non-Archimedean field, Uspehi Mat. Nauk 31 (1976), no. 3(189), 5–70 (Russian). MR 0425030
  • Armand Borel, Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup, Invent. Math. 35 (1976), 233–259. MR 444849, DOI 10.1007/BF01390139
  • N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
  • W. Casselman, Introduction to the theory of admissible representations of $p$-adic reductive groups, preprint.
  • C. W. Curtis, N. Iwahori, and R. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with $(B,$ $N)$-pairs, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 81–116. MR 347996, DOI 10.1007/BF02684695
  • Curtis Greene, Some partitions associated with a partially ordered set, J. Combinatorial Theory Ser. A 20 (1976), no. 1, 69–79. MR 398912, DOI 10.1016/0097-3165(76)90078-9
  • N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of ${\mathfrak {p}}$-adic Chevalley groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5–48. MR 185016, DOI 10.1007/BF02684396
  • David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184. MR 560412, DOI 10.1007/BF01390031
  • Hideya Matsumoto, Analyse harmonique dans les systèmes de Tits bornologiques de type affine, Lecture Notes in Mathematics, Vol. 590, Springer-Verlag, Berlin-New York, 1977 (French). MR 0579177, DOI 10.1007/BFb0086707
  • François Rodier, Décomposition de la série principale des groupes réductifs $p$-adiques, Noncommutative harmonic analysis and Lie groups (Marseille, 1980) Lecture Notes in Math., vol. 880, Springer, Berlin-New York, 1981, pp. 408–424 (French). MR 644842
  • Allan J. Silberger, The Langlands quotient theorem for $p$-adic groups, Math. Ann. 236 (1978), no. 2, 95–104. MR 507262, DOI 10.1007/BF01351383
  • T. A. Springer, Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Invent. Math. 36 (1976), 173–207. MR 442103, DOI 10.1007/BF01390009
  • T. A. Springer and R. Steinberg, Conjugacy classes, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69) Lecture Notes in Mathematics, Vol. 131, Springer, Berlin, 1970, pp. 167–266. MR 0268192
  • Robert Steinberg, Conjugacy classes in algebraic groups, Lecture Notes in Mathematics, Vol. 366, Springer-Verlag, Berlin-New York, 1974. Notes by Vinay V. Deodhar. MR 0352279, DOI 10.1007/BFb0067854
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 277 (1983), 623-653
  • MSC: Primary 22E50; Secondary 12B27, 20G05
  • DOI:
  • MathSciNet review: 694380