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arXiv · 2202.00744

A classification of harmonic weak Maa{\ss} forms of half-integral weight

Claudia Alfes-Neumann·Martin Raum
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Abstract

We classify Harish-Chandra modules generated by the pullback to the metaplectic group of harmonic weak Maa{\ss} forms with exponential growth allowed at the cusps. This extends work by Schulze-Pillot and parallels recent work by Bringmann-Kudla, who investigated the case of integral weights. We realize each of our cases via a regularized theta lift of an integral weight harmonic weak Maa{\ss} form. Harish-Chandra modules in both integral and half-integral weight that occur need not be irreducible. Therefore, our display of the role that the theta lifting takes in this picture, we hope, contributes to an initial understanding of a theta correspondence for extensions of Harish-Chandra modules.

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Claudia Alfes-Neumann, Martin Raum. 2022-02-01. A classification of harmonic weak Maa{\ss} forms of half-integral weight. https://arxiv.org/abs/2202.00744

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