| Abstrakt: |
Let G be the unramified unitary group U(2, 1)(E/F) defined over a non-archimedean local field F of odd residue characteristic p, and let K be a maximal compact open subgroup of G. For an irreducible smooth \overline {\mathbf {F}}_p-representation \pi of G, and a weight \sigma of K contained in \pi, we prove that \pi admits eigenvectors for the spherical Hecke algebra \mathcal {H}(K, \sigma). Our approach is close to that of Barthel–Livné [Duke Math. J. 75 (1994), pp. 261–292] for GL_2. For GL_n (n\geq 3), we give a sketch of an essential case where the analogue of a crucial ingredient in loc.cit fails. [ABSTRACT FROM AUTHOR] |
