Marie-France Vigneras - Representations of GLn(D) Near the Identity

Explore a one-hour lecture on the representations of GLn(D) near the identity, presented by Marie-France Vigneras at the Hausdorff Center for Mathematics. Delve into the extension of Morra's 2013 results for mod p irreducible admissible representations of GL₂(Qp) to inner forms of general linear groups over finite extensions of Qp or Fp((t)). Examine the dimensional properties of these representations with respect to parahoric subgroups and congruence subgroups, and understand the explicit integers involved in the formula dim πKⱼ = a+bpʲ. Gain insights into the collaborative work of Vigneras and Guy Henniart (2023) on this topic, focusing on cases where the coefficient field has characteristic not equal to p.