## Unitary quasilifting: applications

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- by Yuval Z. Flicker PDF
- Trans. Amer. Math. Soc.
**294**(1986), 553-565 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.Â 189â207. With a supplement âOn the notion of an automorphic representationâ by R. P. Langlands. MR**546598** - W. Casselman,
*Characters and Jacquet modules*, Math. Ann.**230**(1977), no.Â 2, 101â105. MR**492083**, DOI 10.1007/BF01370657
L. Clozel, - G. van Dijk,
*Computation of certain induced characters of ${\mathfrak {p}}$-adic groups*, Math. Ann.**199**(1972), 229â240. MR**338277**, DOI 10.1007/BF01429876 - Yuval Z. Flicker,
*Stable and labile base change for $U(2)$*, Duke Math. J.**49**(1982), no.Â 3, 691â729. MR**672503**
â, $L$ - Yuval Z. Flicker,
*On twisted lifting*, Trans. Amer. Math. Soc.**290**(1985), no.Â 1, 161â178. MR**787960**, DOI 10.1090/S0002-9947-1985-0787960-0
â, - 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.Â 141â184. 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., Queenâs Univ., Kingston, Ont., 1977) Queenâs Papers in Pure Appl. Math., No. 48, Queenâs Univ., Kingston, Ont., 1978, pp.Â 281â347. MR**0579175** - H. Jacquet and J. A. Shalika,
*On Euler products and the classification of automorphic representations. I*, Amer. J. Math.**103**(1981), no.Â 3, 499â558. MR**618323**, DOI 10.2307/2374103 - David Keys,
*Principal series representations of special unitary groups over local fields*, Compositio Math.**51**(1984), no.Â 1, 115â130. MR**734788**

*Local base change for*${\text {GL}}(n)$, lectures at IAS, 1984.

*-packets and liftings for*$U(3)$, unpublished, Princton Univ., 1982. â,

*Twisted trace formula and symmetric square comparison*, preprint, Princeton, 1984. â,

*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.

*Unitary quasi-lifting: preparations*, Proc. Conf. on Trace Formula in honor of A. Selberg, Bowdoin, 1984.

## Additional 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