Jacobi and modular forms on symmetric domains
type: Item
instance of: scholarly article
title: Jacobi and modular forms on symmetric domains
zbMATH Open document ID: 1162.11340
author: Min Ho Lee
published in: Rocky Mountain Journal of Mathematics
publication date: 2006-01-24T00:00:00Z
review text: Suppose \(G\) is a semi-simple Lie group of Hermitian type, with associated symmetric domain \({\mathcal D}=G/K\) (\(K\) a maximal compact subgroup), and \(\rho\colon G\to{\text{ Sp}}(n,{\mathbb R})\) is a Lie group homomorphism. Suppose also that \(\tau\colon {\mathcal D}\to {\mathcal H}_n\), where \({\mathcal H}_n\) is the Siegel upper half-plane, is an equivariant map. Then one can define a Jacobi group \(G^J\), a semidirect product \(G\ltimes H\) where \(H\) is the Heisenberg group, and using this one defines Jacobi forms. This paper establishes an isomorphism between the space of Jacobi forms of given weight and certain vector-valued modular forms for \(G\), constructs Eisenstein series for Jacobi forms and writes Jacobi forms in terms of theta functions. The results are fully analogous to this for the symplectic group but the author has performed a public service by working out the details.
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11F55
zbMATH DE Number: 5001004
zbMATH Keywords: Jacobi form
zbMATH Keywords: Eisenstein series
zbMATH Keywords: theta function
reviewed by: G. K. Sankaran
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069683
OpenAlex ID: W2058986308
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DOI: 10.1216/RMJM/1181069683
description: scientific article; zbMATH DE number 5001004