Vector-valued orthogonal modular forms

2022/09/21 by Ma, Shouhei
#11F50 #11F55 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2209.10135

Abstract

This monograph is devoted to the theory of vector-valued modular forms for orthogonal groups of signature (2,n). Our purpose is multi-layered: (1) to lay a foundation of the theory of vector-valued orthogonal modular forms; (2) to develop some aspects of the theory in more depth such as geometry of the Siegel operators, filtrations associated to 1-dimensional cusps, decomposition of vector-valued Jacobi forms, square integrability etc; and (3) as applications derive several types of vanishing theorems for vector-valued modular forms of small weight. Our vanishing theorems imply in particular vanishing of holomorphic tensors of degree

Related

• The theory of vector-modular forms for the modular group
• Symmetric tensor representations,quasimodular forms, and weak Jacobi\n forms
• Constructions of vector-valued modular forms of rank four and level one
• Computations of vector-valued Siegel modular forms
• Classification of Vector-Valued modular Forms of Dimension less than Six