Integral Bases and Invariant Vectors for Weil Representations

Shaul Zemel

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arXiv · 2106.03247

Integral Bases and Invariant Vectors for Weil Representations

Shaul Zemel

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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 $\operatorname{SL}_{2}(\mathbb{Z})$ 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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BibTeX RIS

Shaul Zemel. 2021-06-06. Integral Bases and Invariant Vectors for Weil Representations. https://arxiv.org/abs/2106.03247

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