On twisted lifting

Flicker, Yuval Z.

doi:10.1090/S0002-9947-1985-0787960-0

On twisted lifting

Author: Yuval Z. Flicker
Journal: Trans. Amer. Math. Soc. 290 (1985), 161-178
MSC: Primary 11F70; Secondary 11R39, 11S37, 22E55
DOI: https://doi.org/10.1090/S0002-9947-1985-0787960-0
MathSciNet review: 787960
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If $\sigma$ is a generator of the galois group of a finite cyclic extension of local or global fields, and $\varepsilon$ is a character of ${C_E}( = {E^ \times }\;{\text{or}}\;{E^ \times }\backslash {{\mathbf{A}}^ \times })$ whose restriction to ${C_F}$ has order , then the irreducible admissible or automorphic representations $\pi$ of ${\text{GL}}(n)$ over with $^\sigma \pi \cong \pi \otimes \varepsilon$ are determined.

[A] James G. Arthur, A trace formula for reductive groups. I. Terms associated to classes in 𝐺(𝑄), Duke Math. J. 45 (1978), no. 4, 911–952. MR 518111
[ ${\mathbf{A\prime}}$ ] James Arthur, On a family of distributions obtained from Eisenstein series. II. Explicit formulas, Amer. J. Math. 104 (1982), no. 6, 1289–1336. MR 681738, https://doi.org/10.2307/2374062
[BZ] I. N. Bernstein and A. V. Zelevinsky, Induced representations of reductive 𝔭-adic groups. I, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 4, 441–472. MR 0579172
[B] A. Borel, Automorphic 𝐿-functions, 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. 27–61. MR 546608
[C] P. Cartier, Representations of 𝑝-adic groups: a survey, 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. 111–155. MR 546593
[F] Yuval Z. Flicker, Stable and labile base change for 𝑈(2), Duke Math. J. 49 (1982), no. 3, 691–729. MR 672503
[H] Harish-Chandra, Harmonic analysis on reductive 𝑝-adic groups, Lecture Notes in Mathematics, Vol. 162, Springer-Verlag, Berlin-New York, 1970. Notes by G. van Dijk. MR 0414797
[JS] H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic forms. II, Amer. J. Math. 103 (1981), no. 4, 777–815. MR 623137, https://doi.org/10.2307/2374050
[K] David Kazhdan, On lifting, Lie group representations, II (College Park, Md., 1982/1983) Lecture Notes in Math., vol. 1041, Springer, Berlin, 1984, pp. 209–249. MR 748509, https://doi.org/10.1007/BFb0073149
[Ko] R. Kottwitz, Base change transfer of unit element in Hecke algebra, Lecture at IAS, 1984.
[T] J. Tate, Number theoretic background, 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. 3–26. MR 546607
[Ti] J. Tits, Reductive groups over local fields, 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. 29–69. MR 546588