The explicit Zelevinsky–Aubert duality. Issue 2 (20th February 2023) - Atobe, Hiraku; Mínguez, Alberto
Abstract : In this paper, we give an explicit computable algorithm for the Zelevinsky–Aubert duals of irreducible representations of $p$ -adic symplectic and odd special orthogonal groups. To do this, we establish explicit formulas for certain derivatives and socles. We also give a combinatorial criterion for the irreducibility of certain parabolically induced representations.