Research

Research Statement

My main focus of research is the representation theory of real reductive groups. My current focus is on the geometric side of representation theory: the Orbit Method and unipotent representations. Starting with the Borel-Weil-Bott theorem, we have a geometric realization of representations of complex reductive algebraic groups. With this construction we have a guiding principal to follow: start with representations of smaller groups and build vector bundles on certain homogeneous spaces whose cohomology will be interesting. A large example of such homogeneous spaces are coadjoint orbits of a reductive group on the dual of its Lie algebra. Thus, by starting with a representation Π of the stabilizer G_i of such an orbit O , we obtain a vector bundle V_Π on G/G_i. The pair (O , Π) is a geometric parameter for the group G. One question I work on is the relationship between these parameters and representations of the maximal compact subgroup K of G.

Research Papers

These are broken up by topic.

Undergraduate Thesis