The explicit Zelevinsky-Aubert duality

Abstract

In this paper, we give an explicit computable algorithm for the Zelevinsky-Aubert dual 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.

39 pages

References in corpus (2)

• Homological properties of representations of p-adic groups related to geometry of the group at infinity
• On an algorithm to compute derivatives