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The Contragredient Joint with D. Vogan
 

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
L-homomorphisms 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) = (g-1)
Lemma: There is an automorphism C of LG satisfying: C(g)
is G-conjugate to g-1 for g semisimple
(The Chevalley automorphism, extended to LG)
Lemma: there is an automorphism of WR satisfying: (g) is
WR conjugate to g-1

  

Source: Adams, Jeffrey - Department of Mathematics, University of Maryland at College Park

 

Collections: Mathematics