Distinction of Representations using Buildings for p-adic Groups (Morlet Chair – Dipendra Prasad)
Pairs
CIRM, Luminy, Marseille
https://www.chairejeanmorlet.com/1551.html
Date(s) : 14/03/2016 - 25/03/2016 iCal
0h00
Distinction of Representations using Buildings for p-adic Groups (1551)
Distinction des représentations utilisant des bâtiments pour les groupe p-adic
Dates: 14-25 March 2016 at CIRM (Marseille Luminy, France)
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DESCRIPTION
P. 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 involves Prasad, Broussous and Courtes and interests Heiermann too. 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. |
- Paul Broussous (Université de Poitiers)
- François Courtès (Université de Poitiers) (*)
- Volker Heiermann (I2M, Aix-Marseille Université)
- Dipendra Prasad (TIFR Mumbai)
Regrettably François Courtès passed away in September 2016
– Tribute on Cédric Villani ‘s blog
– Tribute by the World Cube Association, Francocube and Speedcubingfrance.
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