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Previous Up Next Article From References: 2
 

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From References: 2
From Reviews: 1
MR2025061 (2004j:22018) 22E50
Anandavardhanan, U. K. (6-TIFR-SM); Prasad, Dipendra (6-TIFR-SM)
Distinguished representations for SL(2). (English summary)
Math. Res. Lett. 10 (2003), no. 5-6, 867878.
Let G be a reductive p-adic group. A representation of G is called distinguished with respect to
a subgroup H of G if it admits a nontrivial H-invariant 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 p-adic fields. They also compute the dimension of the space of H-invariant linear
forms on G-representations. 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 L-packet.
The authors prove their results by using well-known facts about L-packets 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
E2

  

Source: Anandavardhanan, U. K. - Department of Mathematics, Indian Institute of Technology Bombay

 

Collections: Mathematics