Dan Ciubotaru
Dan Ciubotaru

Ph.D. (2004) Cornell University

First Position
Dissertation
Advisor:
Research Area:
Abstract: One of the fundamental problems in representation theory is the classification of the irreducible unitary representations (the unitary dual) of reductive groups defined over local fields. In the case of groups over padic fields, an important piece of the unitary dual is formed by the Iwahorispherical representations, which are representations with nontrivial fixed vectors under the action of a particular subgroup of G, the Iwahori subgroup.
The main focus of my thesis is the description of the Iwahorispherical unitary representations for a split reductive padic group G of type F_4. From the work of D. Barbasch and A. Moy, this is equivalent to the determination of the unitary representations with real infinitesimal character of the corresponding affine graded Hecke algebra H. Using the classification of simple Hecke algebra modules, the unitary dual is partitioned into subsets parametrized by nilpotent orbits in the dual Lie algebra. Most of the techniques involved are similar to those used by BarbaschMoy and Barbasch in the classification of the spherical unitary spectrum for classical groups.