Generic Mackey Formula for Parahoric Lusztig Functors

TL;DR

This paper proves a generalized Mackey formula for parahoric Lusztig induction in p-adic groups, extending classical results and aiding in understanding the structure of certain representations.

Contribution

It establishes the Mackey formula for parahoric Lusztig induction in the generic case, broadening the theoretical framework for p-adic group representations.

Findings

Proved the Mackey formula for parahoric Lusztig induction in the generic case.

Described the irreducible decomposition of paragoric Deligne-Lusztig representations for elliptic tori.

Extended Lusztig's 1976 results to a broader p-adic context.

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.