Fiona Murnaghan

Reducibility of some Induced Representations of Split Classical p-Adic Groups

In this paper we study reducibility of representations of split classical p-adic groups induced from self-contragredient supercuspidal represetation associated via Howes construction to an admissible character, we show that in many cases Shahidis criterion for reducibility of the induced representation reduces to a simple condition on the admissible character.

κ-types and Γ-asymptotic expansions

Abstract Let G be the k-rational points of a connected reductive k-group, where k is a p-adic field of characteristic zero. We define a notion of strongly good positive G-datum Σ, and construct a κ-type associated to such a datum, following the methods of Yus construction of types. Suppose π is an irreducible admissible representation of G of positive depth, containing such a κ-type. Then assuming that the residual characteristic of k is sufficiently large, we prove that the character of π is Γ-asymptotic on a G-domain defined in terms of Σ, where Γ is a semisimple element naturally associated to Σ. We also obtain a domain of validity for the Shalika germ expansion around the element Γ.

Reducibility of some induced representations of -adic unitary groups

In this paper we study reducibility of those representations of quasi-split unitary p-adic groups which are parabolically induced from supercuspidal representations of general linear groups. For a supercuspidal representation associated via Howe’s construction to an admissible character, we show that in many cases a criterion of Goldberg for reducibility of the induced representation reduces to a simple condition on the admissible character.

Vanishing of coefficients in overlapping germ expansions for p-adic GL(n)

Shalika germs at the identity in p-adic GL(n) will blow up at other singular points. Waldspurger has developed a technique for describing this behaviour at intermediate singular points, giving a «germ expansion for germs». In this paper we discuss which germs occur in such an expansion and fint that the answer is more complicated than expected