Abstract
Finite groups of Lie type, Hecke algebras and p-adic groups all admit an operation on irreducible representations called duality. This operator takes irreducible representations to irreducible representations, often of a much different nature (e.g., the dual of the trivial representation is the Steinberg representation). In this talk, we give a brief history of duality in these contexts, and describe how one might how to explicitly calculate the dual of an irreducible representation for classical p-adic groups.
COinS