Generic Mackey Formula for Parahoric Lusztig Functors

Abstract

Parahoric Lusztig induction gives a broad class of virtual smooth representations of parahoric subgroups in a $p$-adic group, serving as a natural generalization of classical Lusztig induction to the $p$-adic setting. This construction has important applications in the representation theory of p-adic groups. In this paper, we prove the Mackey formula for parahoric Lusztig induction in generic case, which generalizes a classic result of Lusztig in 1976. As an application, we describe the irreducible decomposition of paragoric Deligne-Lusztig representations for the case of elliptic torus.