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MR2025061 (2004j:22018) 22E50
Anandavardhanan, U. K. (6TIFRSM); Prasad, Dipendra (6TIFRSM)
Distinguished representations for SL(2). (English summary)
Math. Res. Lett. 10 (2003), no. 56, 867878.
Let G be a reductive padic group. A representation of G is called distinguished with respect to
a subgroup H of G if it admits a nontrivial Hinvariant linear form. In this paper, the authors
classify H = SL2(F) distinguished representations of G = SL2(E), where E/F is a quadratic
extension of padic fields. They also compute the dimension of the space of Hinvariant linear
forms on Grepresentations. Unlike the case G = GLn(E) and H = GLn(F), which is studied by
various authors, these dimensions can be bigger than 1 and can vary within an Lpacket.
The authors prove their results by using wellknown facts about Lpackets of SL2(E) and about
GL2(F)distinguished representations of GL2(E), and analyzing the restrictions of representa
tions of GL2(E) to GL2(E)+
, where GL2(E)+
= {g GL2(E)  det g F×
E×2
