On the symmetric square. Unstable Twisted Characters

Details On the symmetric square. Unstable Twisted Characters On the symmetric square. Unstable Twisted Characters

2007-11-28

arxiv.org/abs/0711.4447v1

Israel Journal of Mathematics, 134 (2003), 307--316

Mathematics

Representation Theory

8 pages

Scientific paper

We provide a purely local computation of the (elliptic) twisted (by "transpose-inverse") character of the representation \pi=I(\1) of PGL(3) over a p-adic field induced from the trivial representation of the maximal parabolic subgroup. This computation is independent of the theory of the symmetric square lifting of [IV] of automorphic and admissible representations of SL(2) to PGL(3). It leads to a proof of the (unstable) fundamental lemma in the theory of the symmetric square lifting, namely that corresponding spherical functions (on PGL(2) and PGL(3)) are matching: they have matching orbital integrals.

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