Tuesday 16 June 2026, 16:00 - 17:00 in HG03.085
Janet Flikkema (Radboud)
Covering groups of reductive p-adic groups and their representation theory
In my talk, I aim to give an accessible overview of my PhD research, where I studied smooth complex representations of covers of reductive p-adic groups. An example of such a covering group is the metaplectic group, which is a double cover of the symplectic group. The metaplectic group fits into a more general framework developed by Brylinski and Deligne. The first part of my talk gives an introduction to (Brylinski-Deligne) covers of reductive p-adic groups, with some examples. After that, I will move on to the representation theory. The main result of my PhD research is a formula for the Harish-Chandra mu-function for covering groups, which is defined using intertwining operators between parabolically induced representations. This result is joint with Solleveld and generalizes Silberger's formula for reductive groups, however the proof is different. I will present this result, together with the necessary context and motivation. Finally, I will discuss additional results and further directions, in particular regarding the structure of Bernstein blocks for principal series representations of BD covers.