| Résume | In joint work with A.-M. Aubert and B. Romano, we define an involution on the space of compact tempered unipotent representations of inner twists of a split simple p-adic group. This generalizes a construction by Waldspurger for elliptic tempered representations of split orthogonal groups. We conjecture that the restriction to reductive quotients of maximal compact open subgroups intertwines this involution with a disconnected version of Lusztig's nonabelian Fourier transform for finite reductive groups. I will explain the definitions, the relation with Lusztig's proposed unipotent almost characters of semisimple p-adic groups, and give supporting evidence for the conjectures. |
