Primary Areas of Interest:
- Lie Algebras
- Representation Theory
- Combinatorics
- Education
Representation Theory, Lie Algebras, and Combinatorics:
My thesis examines Demazure modules of the quantum group associated with the affine special linear algebra. Demazure modules of quantum groups are finite subspaces of integrable modules, which are infinite dimensional. These Demazure modules are particularly nice since their union gives the entire integrable module. In order to understand these modules, I use colored Young diagrams to draw crystal graphs of these modules. Here is an example of a partial crystal graph of one of these modules:
The portion in red is the crystal graph Br1r0(2Lambda0)
which corresponds to a specific Demazure module of the integrable modules of highest weight 2Lambda0. The whole picture is a subset of the crystal graph of this integrable module.