Integral bases and invariant vectors for Weil representations

Shaul Zemel

doi:10.1007/s40993-022-00413-x

Integral bases and invariant vectors for Weil representations

Shaul Zemel^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English
Article number	5
Journal	Research in Number Theory
Volume	9
Issue number	1
DOIs	https://doi.org/10.1007/s40993-022-00413-x
State	Published - Mar 2023

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Invariant Subspaces
Representations over Rings
Weil Representations

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10.1007/s40993-022-00413-x

Cite this

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Integral bases and invariant vectors for Weil representations

Abstract

Bibliographical note

Keywords

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