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MR2146859 (2006g:22013) 22E50 (11F70 20G25 22E35)
Anandavardhanan, U. K. (6-TIFR-SM); Rajan, C. S. (6-TIFR-SM)
Distinguished representations, base change, and reducibility for unitary groups.
Int. Math. Res. Not. 2005, no. 14, 841854.
A representation (, V ) of a group G is distinguished with respect to a character of a subgroup
H if there exists a nonzero linear form f V
such that f((h)v) = (h)f(v) for every h
H, v V . Let E be a quadratic extension of a p-adic field F. The aim of the paper under review is
to explore distinguishedness of representations of G = GLn(E) with respect to characters of H =
GLn(F). The following results are proved:
(1) A supercuspidal representation of GL3(E) is distinguished with respect to GL3(F), if and
only if it is a stable base change lift from U(3). This confirms a conjecture by Y. Z. Flicker
[J. Reine Angew. Math. 418 (1991), 139172; MR1111204 (92i:22019)], who treated GL2.
(2) Let E/F be the quadratic character of F×
associated with the extension E. Let P be a
maximal parabolic subgroup of U(n, n) with Levi component isomorphic to GLn(E), and