Restriction of modular forms on E_7,3 to Sp₆

2025/02/20 by Henry H. Kim, Kim, Henry H, Takuya Yamauchi +1
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2502.14554

openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the restriction of modular forms such as Ikeda type lifts and the Eisenstein series on the exceptional group of type E_7,3 to the symplectic group Sp₆ (rank 3). As an application, we explicitly write down the restriction when modular forms have small weight. The restriction may contain Miyawaki lifts of type I,II (CAP forms) and genuine forms whose description is compatible with Arthur's classification.

Related

• Period of the Ikeda type lift for E_7,3
• Higher level cusp forms on the exceptional group of type E₇
• Modular forms on indefinite orthogonal groups of rank three
• Twisted Koecher-Maass series of the Ikeda type lift for the exceptional group of type E_7,3
• Siegel modular forms and finite symplectic groups