Integral bases and invariant vectors for Weil representations

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Abstract

We construct, for the Weil representation associated with any discriminant form, an explicit basis in which the action of the representation involves algebraic integers over its field of definition. The action of a general element of SL 2(Z) on many parts of these bases is simple and explicit, a fact that we use for determining the dimension of the space of invariants for some families of discriminant forms.

Original languageAmerican English
Article number5
JournalResearch in Number Theory
Volume9
Issue number1
DOIs
StatePublished - Mar 2023

Keywords

  • Invariant Subspaces
  • Representations over Rings
  • Weil Representations

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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