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.

 

Unitary quasilifting: applications
HTML articles powered by AMS MathViewer

by Yuval Z. Flicker
Trans. Amer. Math. Soc. 294 (1986), 553-565
DOI: https://doi.org/10.1090/S0002-9947-1986-0825721-5
PDF | Request permission

Abstract:

Let $U(3)$ be the quasi-split unitary group in three variables defined using a quadratic extension $E/F$ of number fields. Complete local and global results are obtained for the $\sigma$-endo-(unstable) lifting from $U(2)$ to ${\text {GL}}(3, E)$. This is used to establish quasi-(endo-)lifting for automorphic forms from $U(2)$ to $U(3)$ by means of base change from $U(3)$ to ${\text {GL}}(3, E)$. Base change quasi-lifting is also proven. Continuing the work of $\left [ {\mathbf {I}} \right ]$, the exposition is elementary, and uses only a simple form of an identity of trace formulas, and base change transfer of orbital integrals of spherical functions.
References
  • A. Borel and H. Jacquet, Automorphic forms and automorphic representations, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 189–207. With a supplement “On the notion of an automorphic representation” by R. P. Langlands. MR 546598
  • W. Casselman, Characters and Jacquet modules, Math. Ann. 230 (1977), no. 2, 101–105. MR 492083, DOI 10.1007/BF01370657
    • L. Clozel, Local base change for ${\text {GL}}(n)$, lectures at IAS, 1984.
  • G. van Dijk, Computation of certain induced characters of ${\mathfrak {p}}$-adic groups, Math. Ann. 199 (1972), 229–240. MR 338277, DOI 10.1007/BF01429876
  • Yuval Z. Flicker, Stable and labile base change for $U(2)$, Duke Math. J. 49 (1982), no. 3, 691–729. MR 672503
    • —, $L$-packets and liftings for $U(3)$, unpublished, Princton Univ., 1982. —, Twisted trace formula and symmetric square comparison, preprint, Princeton, 1984. —, Symmetric square: Applications of a trace formula, preprint, Princeton, 1984. See also: Outer automorphisms and instability, ThĂ©orie de Nombres, Paris, 1980-1981, Progress in Math., vol. 22, BirkhĂ€user, Basel, 1982, pp. 57-65.
  • Yuval Z. Flicker, On twisted lifting, Trans. Amer. Math. Soc. 290 (1985), no. 1, 161–178. MR 787960, DOI 10.1090/S0002-9947-1985-0787960-0
    • —, Unitary quasi-lifting: preparations, Proc. Conf. on Trace Formula in honor of A. Selberg, Bowdoin, 1984.
  • Stephen Gelbart and Ilya Piatetski-Shapiro, Automorphic forms and $L$-functions for the unitary group, Lie group representations, II (College Park, Md., 1982/1983) Lecture Notes in Math., vol. 1041, Springer, Berlin, 1984, pp. 141–184. MR 748507, DOI 10.1007/BFb0073147
  • Harish-Chandra, Admissible invariant distributions on reductive $p$-adic groups, Lie theories and their applications (Proc. Ann. Sem. Canad. Math. Congr., Queen’s Univ., Kingston, Ont., 1977) Queen’s Papers in Pure and Appl. Math., No. 48, Queen’s Univ., Kingston, Ont., 1978, pp. 281–347. MR 0579175
  • H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic representations. I, Amer. J. Math. 103 (1981), no. 3, 499–558. MR 618323, DOI 10.2307/2374103
  • David Keys, Principal series representations of special unitary groups over local fields, Compositio Math. 51 (1984), no. 1, 115–130. MR 734788
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 11F70, 22E55
  • Retrieve articles in all journals with MSC: 11F70, 22E55
Bibliographic Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 553-565
  • MSC: Primary 11F70; Secondary 22E55
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0825721-5
  • MathSciNet review: 825721