On the Internal Structure of Parahoric Subgroups
Benedict Gross, Harvard University
We will discuss the structure of parahoric subgroups in the simplest case — for a split, simple, simply-connected group over a local field. In particular, we will describe a result of Reeder and Yu which identifies the representations which occur as subquotients of the Moy-Prasad filtration with the summands in a Z/dZ-grading of the Lie algebra over the residue field. This provides a useful connection between the theory of Bruhat-Tits and the invariant theory of Vinberg.
Please see also: Professor Gross's e-print Parahorics (PDF).