Tuesday 26th of November 2024, 13:30-14:30 in HG03.085
Janet Flikkema
Poles and zeros of the Harish-Chandra \(\mu\)-function for covering groups of reductive \(p\)-adic groups
In my talk, I will attempt to explain my research project, which is about poles and zeros of the Harish-Chandra \(\mu\)-function. This function appears in the representation theory of \(p\)-adic groups, for example in a Plancherel formula for reductive \(p\)-adic groups. It can also be used to describe Bernstein blocks in the category of smooth representations of a reductive \(p\)-adic group. This work was done by my supervisor Maarten Solleveld, and the goal is to generalize these results to covering groups of reductive \(p\)-adic groups. There is a formula for the \(\mu\)-function given by Silberger, but it is not clear how his proof generalizes to covering groups. Therefore, Maarten and I have been working on a different proof, which does work for covering groups of reductive p-adic groups.
There are quite a few ingredients that come into play: (covering groups of) reductive \(p\)-adic groups; representation theory and the Bernstein decomposition; intertwining operators and the \(\mu\)-function. I also hope to say a little bit about the proof of the formula of the \(\mu\)-function. But as I'm writing this and preparing my talk, I realize it will probably be a bit ambitious to try and explain everything. So let's see what selection I will have come up with next Tuesday!