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Mathematical Research Letters 10, 110 (2003) DISTINGUISHED REPRESENTATIONS FOR SL(2)

Summary: Mathematical Research Letters 10, 110 (2003)
U.K. Anandavardhanan and Dipendra Prasad
Abstract. Let E/F be a quadratic extension of p-adic fields. We compute the
multiplicity of the space of SL2(F)-invariant linear forms on a representation of
SL2(E). This multiplicity varies inside an L-packet similar in spirit to the multi-
plicity formula for automorphic representations due to Labesse and Langlands.
1. Introduction
A representation of a group G is said to be distinguished with respect to
a subgroup H of G if it admits a non-trivial H-invariant linear form. More
generally if is a character of H, we say that is -distinguished if there is
a non-trivial linear form on the space of on which H operates via , i.e.
: - C such that
((h)v) = (h) (v)
for all h H, v . This concept is specially useful when H is the fixed points
of an involution on G. Classifying distinguished representations for both local
and global fields has been an important and very active area of research in the
last few years, cf. [A-T], [F], [H], [H-Ma], [H-Mu1], [H-Mu2], [J-Y1], [J-Y2],
[J-R], [P3], [P4]. All these works are for the case G = GL(n), and H one of the
classical groups.


Source: Anandavardhanan, U. K. - Department of Mathematics, Indian Institute of Technology Bombay
Prasad, Dipendra - School of Mathematics, Tata Institute of Fundamental Research


Collections: Mathematics