On the weighted fundamental lemma for twisted endoscopy of the general linear group
Abstract: We present a conjecture asserting an identity between stable weighted
orbital integrals on the groups Sp(2n) and SO(2n+1). We show that this conjecture, together
with the weighted fundamental lemma for standard endoscopy, implies the twisted weighed fundamental
for GL(n) with respect to the transpose inverse automorphism. In particular this allows us to
deduce, from results in the literature, the twisted weighted fundamental lemma necessary to
understand the lifting of automorphic representations from SO(5) to GL(4) and from Sp(4)
to GL(5).
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