Dan Ciubotaru

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 p-adic fields, an important piece of the unitary dual is formed by the Iwahori-spherical 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 Iwahori--spherical unitary representations for a split reductive p-adic 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 Barbasch-Moy and Barbasch in the classification of the spherical unitary spectrum for classical groups.