In 1980, Zelevinsky studied representation theory for p-adic general linear groups. He gave an involution on the set of irreducible representations, which exchanges the trivial representation with the Steinberg representation. Aubert extended this involution to p-adic reductive groups, which is now called the Zelevinsky-Aubert duality. It is expected that this duality preserves the unitarity.
In this talk, we explain an algorithm to compute the Zelevinsky-Aubert duality for odd special orthogonal groups or symplectic groups.
This is a joint work with Alberto Minguez.
Slides for the talk are available below