Ramified Satake Isomorphisms for strongly parabolic characters

TL;DR

This paper establishes Satake-type isomorphisms for strongly parabolic characters of the compact torus in reductive p-adic groups, extending classical results to a broader class of characters.

Contribution

It introduces the concept of strongly parabolic characters and proves generalized Satake isomorphisms for these characters, broadening the scope of existing theory.

Findings

Proved Satake-type isomorphisms for strongly parabolic characters.

Generalized classical Satake, Howe, Bushnell-Kutzko, and Roche results.

Extended the framework of harmonic analysis on p-adic groups.

Abstract

For certain characters of the compact torus of a reductive $p$-adic group, which we call strongly parabolic characters, we prove Satake-type isomorphisms. Our results generalize those of Satake, Howe, Bushnell and Kutzko, and Roche.