**Vincent Secherre**

Universite de Versailles Saint-Quentin, France

January 18, 2018

**Linked representations of finite and p-adic general linear groups**:
I will introduce an equivalence relation, called linkedness, between irreducible representations of general linear groups, that generalizes the relation of congruence mod a prime number. For
finite general linear groups, all irreducible representations appear to be linked. For p-adic general linear groups, the notion of linkedness unexpectedly appears to be related to an invariant coming from Bushnell-Kutzko’s type theory. I will explain this and, if time permits, I will explain the consequences of this for the Jacquet-Langlands correspondence.