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MR2391809 (2009i:22025) 22E50 (20G25 22E35)
Murnaghan, Fiona (3TRNT)
Spherical characters: the supercuspidal case. (English summary)
Group representations, ergodic theory, and mathematical physics: a tribute to George W.Mackey,
301313, Contemp.Math., 449, Amer.Math.Soc., Providence, RI, 2008.
Let G be a connected reductive padic group. Let be an involution of G and let H be a reductive
padic group that is a subgroup of the fixed group G
containing the identity component of G
.
Then G/H is a reductive padic symmetric space. Many results in harmonic analysis on G have
some kind of analogues in harmonic analysis on G/H.
An irreducible admissible representation of G is said to be distinguished (with respect to H)
if it admits a nontrivial Hinvariant linear form. From now on, consider representations such
that both and it dual are distinguished. Let HomH(, 1) and HomH(, 1). For f
C
c (G), define (f) = (, (f)). Then is an Hbiinvariant distribution and this is called
