A representation theoretic approach to Kohnen's plus space of modular forms of half integral weight

TL;DR

This paper develops a representation theoretic framework for the two-fold central extension of SL(2) over 2-adic numbers, establishing a local Shimura correspondence compatible with the global one at p=2.

Contribution

It introduces a new representation theoretic approach to the plus space of modular forms of half integral weight, connecting local and global Shimura correspondences.

Findings

Established a local Shimura correspondence for the two-fold central extension of SL(2)

Proved compatibility of local and global Shimura correspondences at p=2

Developed representation theory for the 2-adic central extension of SL(2)

Abstract

In this paper we develop representation theory of the two fold central extension of SL(2) over the field of 2-adic numbers. As a consequence, we obtain a local Shimura correspondence between the two fold central extension of SL(2) and the linear group PGL(2), which we show to be compatible with the global Shimura correspondence at p=2.