Geometry Seminar

For general linear groups, one can prove a weak form of the categorical local Langlands correspondence by a certain "reduction to unipotent parameters". The key point is that for such groups an arbitrary component of the moduli space of Langlands parameters is isomorphic to a distinguished "unipotent" component of the space of parameters parameters for a smaller general linear group. For more general groups this is no longer true: there is still a relationship between the geometry of the two components but it is more subtle. We will show how to use this relationship to establish certain special cases of the categorical local Langlands correspondence for classical groups.