 
Summary: IMRN International Mathematics Research Notices
2005, No. 14
Distinguished Representations, Base Change,
and Reducibility for Unitary Groups
U. K. Anandavardhanan and C. S. Rajan
1 Introduction
A representation (, V) of a group G is said to be distinguished with respect to a char
acter of a subgroup H if there exists a linear form l of V satisfying l((h)v) = (h)l(v)
for all v V and h H. When the character is taken to be the trivial character, such
representations are also called as distinguished representations of G with respect to H.
The concept of distinguished representations can be carried over to a continuous con
text of representations of real and padic Lie groups, as well in a global automorphic
context (where the requirement of a nonzero linear form is replaced by the nonvanishing
of a period integral). The philosophy, due to Jacquet, is that representations of a group
G distinguished with respect to a subgroup H of fixed points of an involution on G are
often functorial lifts from another group G .
In this paper, we consider G = ResE/F GL(n) and H = GL(n), where E is a qua
dratic extension of a nonArchimedean local field F of characteristic zero. In this case,
the group G is conjectured to be the quasisplit unitary group with respect to E/F,
G = U(n) = g GLn(E)  gJt
