An explicit computation of p-stabilized vectors

TL;DR

This paper presents a method for explicitly computing p-stabilized vectors in the context of p-adic groups, with applications to global automorphic forms including a specific example involving Saito-Kurokawa lifts.

Contribution

It introduces a new explicit computational method for p-stabilized vectors in parahori-fixed spaces, extending to global automorphic forms.

Findings

Explicit p-stabilized form of a Saito-Kurokawa lift provided

Method for computing p-stabilized vectors in p-adic groups developed

Application to global automorphic forms discussed

Abstract

In this paper, we give a method to compute p-stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over p-adic fields. The application to the global setting is also discussed. In particular, we give an explicit p-stabilized form of a Saito-Kurokawa lift.