2007-10-12
Susana Salamanca, New Mexico State University
On the Omega-regular Unitary Dual of the Metaplectic Group
In this talk we formulate a conjecture about the unitary dual of the
metaplectic group. We prove this conjecture for the case of Mp(4,R)
and present some interesting cases occurring in higher rank. The work is
joint with A. Pantano and A. Paul. The result is a strengthening, for
this case, of the following result: any unitary representation of a
real reductive Lie group with strongly regular infinitesimal character can
be obtained by cohomological induction from a one dimensional
representation. Strongly regular representations are those whose
infinitesimal character is at least as regular as that of the trivial
representation. We are extending the result to representations with
omega-regular infinitesimal character: those whose infinitesimal
character is at least as regular as that of the oscillator
representation. The proof uses results of Parthasarathy's and work of
Barbasch and Pantano on the signature of an intertwining operator to
establish nonunitarity.