Computing Invariants of the Weil representation

2017/05/12 by Stephan Ehlen, Ehlen, Stephan, Nils-Peter Skoruppa +1
Computer Science · Mathematics · #11F27 #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.1705.04572

openalex publication_date 2017/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an algorithm for computing bases and dimensions of spaces of invariants of Weil representations of SL₂(ℤ) associated to finite quadratic modules. We prove that these spaces are defined over ℤ, and that their dimension remains stable if we replace the base field by suitable finite prime fields.

Related

• Integral Bases and Invariant Vectors for Weil Representations
• Weil representations associated to finite quadratic modules
• The basis problem for modular forms for the Weil representation
• Jacobi Forms of Degree One and Weil Representations
• The invariants of the Weil representation of SL₂(ℤ)