Integral Bases and Invariant Vectors for Weil Representations

2021/06/06 by Zemel, Shaul · 1 citation
#11F27 #FOS: Mathematics #Number Theory (math.NT) #maybe 20C10

paper · doi:10.48550/arxiv.2106.03247

Abstract

We show that the Weil representation associated with any discriminant form admits a basis in which the action of the representation involves algebraic integers. The action of a general element of SL₂(ℤ) on many parts of these bases is simple an explicit, a fact that we use for determining the dimension of the space of invariants for some families of discriminant forms.

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• Hilbert Eisenstein series as Doi-Naganuma lift

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• The basis problem for modular forms for the Weil representation
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• The invariants of the Weil representation of SL₂(ℤ)
• Jacobi Forms of Degree One and Weil Representations