Emmy-Noether-Seminar: Regularity theorems for invariant eigendistributions on reductive symmetric spaces

Regularity theorems for invariant eigendistributions on reductive symmetric spaces

Jannik Michel (Padreborn)

Abstract: Harish-Chandra’s celebrated regularity theorem states that a conjugation invariant distribution on a reductive group G which is eigen for the algebra of biinvariant differential operators of G (for example the distributional character of an irreducible unitary representation) is necessarily a locally integrable function on G that is real analytic on the regular set. It is the technical cornerstone on which Harish-Chandra’s original proof of the existence and exhaustion of the discrete series representations is based upon. In this talk I will present an analogue of Harish-Chandra’s regularity theorem for reductive symmetric spaces.