 
Summary: The Contragredient
Joint with D. Vogan
Spherical Unitary Dual for Complex Classical Groups
Joint with D. Barbasch
The Contragredient
Problem: Compute the involution of the space of
Lhomomorphisms corresponding to (the
contragredient)
i.e. : W
F LG, what ?
(Assume known. . . )
(Well defined, same for all ?)
Nowhere to be found ("much needed gap in the literature"),
even for F = R
Character: (g) = (g1)
Lemma: There is an automorphism C of LG satisfying: C(g)
is Gconjugate to g1 for g semisimple
(The Chevalley automorphism, extended to LG)
Lemma: there is an automorphism of WR satisfying: (g) is
WR conjugate to g1
