# Supersingular representations of unramified U(2,1)

`2018-05-16 10:30:00``2018-05-16 11:30:00``Supersingular representations of unramified U(2,1)``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/supercuspidal representations. However, supersingular representations remain mysterious largely, and in general we know them very little. So far, there are only classifications 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 via a local method 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).``Third floor seminar room``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`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/supercuspidal representations. However, supersingular representations remain mysterious largely, and in general we know them very little. So far, there are only classifications 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 via a local method 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).

Last Updated Date : 08/05/2018