Gilbert Moss (UMaine)

Harish-Chandra envisioned generalizations of the Plancherel formula in the representation theory of p-adic reductive groups, involving integration with the Plancherel measure, a function constructed using intertwining operators between parabolically induced representations. In the last several decades, it has become apparent that many of the analytic tools used to build this theory can be replaced with purely algebraic constructions. In this talk we describe recent work where we push the algebraic framework further to construct intertwining operators and the Plancherel measure for representations with coefficients in arbitrary commutative Noetherian Z[1/\sqrt{p}]-algebras. This generalizes constructions of Waldspurger, Dat, and Girsch. We prove a generic Schur’s lemma result, which circumvents the need for generic irreducibility in defining the j-function. Finally, we will describe an application using the j-function to characterize a putative local Langlands correspondence in families for classical groups.