Nearly holomorphic automorphic forms on SL₂

2019/12/10 by Shuji Horinaga, Horinaga, Shuji
Mathematics · #Advanced Algebra and Geometry #Geometry and complex manifolds #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1912.04552

Abstract

We define the space of nearly holomorphic automorphic forms on a connected reductive group G over ℚ such that the homogeneous space G(ℝ)¹/ K_∞^∘ is a Hermitian symmetric space. By Pitale, Saha and Schmidt's study, there are the classification of indecomposable (\mathfrakg,K_∞)-modules which occur in the space of nearly holomorphic elliptic modular forms and Siegel modular forms of degree 2. This paper studies global representations of the adele group G(\mathbbA_ℚ) which occur in the space of nearly holomorphic Hilbert modular forms. In the case of elliptic modular forms, the result of this paper is an adelization of Pitale, Saha and Schmidt's result.

Related

• Representations of SL₂(R) and nearly holomorphic modular forms
• Nearly holomorphic Drinfeld modular forms and their special values at CM points
• Quasi-modular forms attached to Hodge structures
• Maass spaces on U(2,2) and the Bloch-Kato conjecture for the symmetric square motive of a modular form
• Adelic Maass spaces on U(2,2)