Nilpotent orbits and tilting modules for the general linear group
This talk is about a certain class of finite-dimensional representations (called "tilting modules") for the group GL_n(k), where k is an algebraically closed field of positive characteristic. Here are some things one can do with these modules: (1) Classify the tensor ideals of tilting modules (this makes sense because the tilting modules are closed under tensor product). (2) Compute their support varieties, which are closures of nilpotent orbits in the Lie algebra of GL_n. I will explain what is known about these questions, and I will discuss a conjectural link between them, with some concrete examples. This is joint work with W. Hardesty and S. Riche.