**RESEARCH IN PAIRS**

**Distinction of Representations using Buildings for**

*p-*adic Groups (1551)**Dates : 14-25 March 2016 at CIRM (Marseille Luminy, France)**

## DescriptionP. Broussous and F. Courtes have used buildings to prove a conjecture of Dipendra Prasad, Duke Math. J. (2001) regarding the distinction of the Steinberg representation of
G( E) by G( F) where E /F is a quadratic extension of p-adic fields.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 with involve Prasad, Broussous and Courtes and will interest Heiermann too. We will get together to learn about sorne 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 quasi-split groups. 'We would like to think about it for general reductive groups where the notion of Steinberg is of course as meaningful. Bibliography (1) D. Prasad: On a conjecture of Jacquet about distinguished representations of GL(n), Duke Math Journal, vol. 109, N°1, (2001), pp. 67 - 78.(2) P. Broussous, F. Courtes, Distinction of the Steinberg representation. Int. Math. Res. Notices, (2014), no. 11, pp. 3140-3157.(3 ) F. Courtes, Distinction of the Steinberg representation II: an equality of characters; to appear in Forum Mathematicum.(4) F. Courtes, Distinction of the Steinberg representation III; the tamely ramified case; preprint. |
## Participants
- Paul Broussous (Université de Poitiers)
- François Courtès (Université de Poitiers) (
***)
- Volker Heiermann (I2M, Aix-Marseille Université)
- Dipendra Prasad (TIFR Mumbai)
* In Memoriam Regretably François Courtès passed away in September 2016 - Tribute on Cédric Villani 's blog - Tribute by the World Cube Association, Francocube and Speedcubingfrance. Sponsor |