Distinction of Representations using Buildings for p-adic Groups (Morlet Chair – Dipendra Prasad)

The proof, although still not in all cases, uses novel application of Harmonic analysis on the building, basically a theorem of Borel-Serre realizing the Steinberg representation on the top  dimensional cohomology (with  compact  support) of the building. It is likely that this way of proving theorem for the Steinberg representation  can be substantially generalized.

The proposed research in pairs involves Prasad, Broussous and Courtes and interests Heiermann too.
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We will get together to learn about some details of the proof (and buildings in general) that Broussous and Courtes have made, and to think about the more general conjectures. The proposed conjecture of D. Prasad was only for quasi-split groups, but he has realised over the years that there is no reason to restrict oneself to quasisplit groups.  ‘We would like to think about it for general  reductive groups where the notion of Steinberg is of course as meaningful ».