Skip to Main Content

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 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An explicit Plancherel formula for $\textrm {U}(2,1)$
HTML articles powered by AMS MathViewer

by David Jabon, C. David Keys and Allen Moy
Trans. Amer. Math. Soc. 341 (1994), 157-171
DOI: https://doi.org/10.1090/S0002-9947-1994-1106191-3

Abstract:

The admissible duals of quasi-split unitary groups over nonarchimedean fields are determined. The set of irreducible unitarizable representations, and the Plancherel measure on the unitary dual, is given explicitly.
References
  • Armand Borel and Nolan R. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Mathematics Studies, No. 94, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 554917
  • Laurent Clozel, Sur une conjecture de Howe. I, Compositio Math. 56 (1985), no. 1, 87–110 (English, with French summary). MR 806844
  • Laurent Clozel, Orbital integrals on $p$-adic groups: a proof of the Howe conjecture, Ann. of Math. (2) 129 (1989), no. 2, 237–251. MR 986793, DOI 10.2307/1971447
  • Harish-Chandra, The Plancherel formula for reductive $p$-adic groups (and corrections), Collected Papers, Vol. 4, pp. 353-370, preprint. R. Howe and A. Moy, Harish-Chandra homomorphisms for $p$-adic groups, CBMS Regional Conf. Ser. in Math., vol. 59, Amer. Math. Soc., Providence, R.I., 1985. —, Minimal $K$-types for $G{l_n}$ over $p$-adic field, Orbites Unipotentes et Représentations, Vol. II: Groupes $p$-Adiques et Réels, Astérique, no. 171-172, 1989. D. Jabon, The supercuspidal representations of $U(2,1)$ and $GS{p_4}$ over a local field via Hecke algebra isomorphisms, Thesis, Univ. of Chicago, 1989.
  • David Keys, Principal series representations of special unitary groups over local fields, Compositio Math. 51 (1984), no. 1, 115–130. MR 734788
  • C. David Keys and Freydoon Shahidi, Artin $L$-functions and normalization of intertwining operators, Ann. Sci. École Norm. Sup. (4) 21 (1988), no. 1, 67–89. MR 944102
  • Anthony W. Knapp, Representation theory of semisimple groups, Princeton Mathematical Series, vol. 36, Princeton University Press, Princeton, NJ, 1986. An overview based on examples. MR 855239, DOI 10.1515/9781400883974
  • Robert P. Langlands, On the functional equations satisfied by Eisenstein series, Lecture Notes in Mathematics, Vol. 544, Springer-Verlag, Berlin-New York, 1976. MR 0579181
  • I. G. Macdonald, Spherical functions on a group of $p$-adic type, Publications of the Ramanujan Institute, No. 2, University of Madras, Centre for Advanced Study in Mathematics, Ramanujan Institute, Madras, 1971. MR 0435301
  • Lawrence Morris, Tamely ramified supercuspidal representations of classical groups. I. Filtrations, Ann. Sci. École Norm. Sup. (4) 24 (1991), no. 6, 705–738. MR 1142907
  • Allen Moy, Representations of $\textrm {U}(2,1)$ over a $p$-adic field, J. Reine Angew. Math. 372 (1986), 178–208. MR 863523, DOI 10.1515/crll.1986.372.178
  • Gopal Prasad and M. S. Raghunathan, Topological central extensions of semisimple groups over local fields, Ann. of Math. (2) 119 (1984), no. 1, 143–201. MR 736564, DOI 10.2307/2006967
  • Freydoon Shahidi, A proof of Langlands’ conjecture on Plancherel measures; complementary series for $p$-adic groups, Ann. of Math. (2) 132 (1990), no. 2, 273–330. MR 1070599, DOI 10.2307/1971524
  • Allan J. Silberger, Introduction to harmonic analysis on reductive $p$-adic groups, Mathematical Notes, vol. 23, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1979. Based on lectures by Harish-Chandra at the Institute for Advanced Study, 1971–1973. MR 544991
  • Allan J. Silberger, Special representations of reductive $p$-adic groups are not integrable, Ann. of Math. (2) 111 (1980), no. 3, 571–587. MR 577138, DOI 10.2307/1971110
  • Allan J. Silberger, Complementary series for $p$-adic groups. I, Trans. Amer. Math. Soc. 259 (1980), no. 2, 589–598. MR 567099, DOI 10.1090/S0002-9947-1980-0567099-5
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E50, 11F70
  • Retrieve articles in all journals with MSC: 22E50, 11F70
Bibliographic Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 341 (1994), 157-171
  • MSC: Primary 22E50; Secondary 11F70
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1106191-3
  • MathSciNet review: 1106191