Matrix generators for Weil representations

2025/10/14 by Korhonen, Mikko
#20C99 #20H20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.12261

Abstract

Let r be an odd prime and \mathbbF a field containing a primitive rth root of unity. Then for all ℓ ≥ 1, there is a faithful representation f: Sp_2ℓ(r) → GL_r^ℓ(\mathbbF) called the Weil representation. We provide explicit matrices generating Sp_2ℓ(r) in GL_r^ℓ(\mathbbF), which we have implemented in Magma. We also describe such generators for the irreducible Weil representations of Sp_2ℓ(r), which are of degree (r^ℓ ± 1)/2 and arise as irreducible constituents of the Weil representations.

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