The recent work of Abe--Henniart--Herzig--Vigneras gives a classification of irreducible admissible mod-$p$ representations of a $p$-adic reductive group in terms of supersingular representations. However, supersingular representations remain mysterious largely, and in general we know them very little. Up to date, there are only a classification of them for the group $GL_2 (Q_p)$ and a few other closely related cases. In this talk, we will present some work on the unramified unitary group $G=U(2, 1)$ defined over a non-archimedean local field of odd residue characteristic $p$, in which we show the pro-$p$-Iwahori invariants of certain supersingular representations of $G$, as right modules over the pro-$p$-Iwahori--Hecke algebra of $G$, are not simple. This gives a large amount of examples which unveils a possible new feature of supersingular representations in general (note that such a phenomenon never happens in complex representations). All are welcome.
Mon, 11/06/2018 - 14:00 to 15:00
Room 70A, Ross Building, Jerusalem, Israel