Resumen de Waldspurger's involution and types

David Manderscheid

• Waldspurger's involution for the genuine irreducible supercuspidal representations of is parametrized in terms of types in the case -adic with odd. In particular, it is shown that the in-volution is given by conjugating by an element of and twisting one of the defining parameters of an associated type by a quadratic character, the relevant parameter being a character on the norm one elements of a quadratic extension.