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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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

Keywords

Invariant Subspaces
Representations over Rings
Weil Representations

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s40993-022-00413-x

Cite this

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title = "Integral bases and invariant vectors for Weil representations",

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.",

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AU - Zemel, Shaul

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N2 - 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.

AB - 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.

KW - Invariant Subspaces

KW - Representations over Rings

KW - Weil Representations

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U2 - 10.1007/s40993-022-00413-x

DO - 10.1007/s40993-022-00413-x

M3 - مقالة

SN - 2363-9555

VL - 9

JO - Research in Number Theory

JF - Research in Number Theory

IS - 1

M1 - 5

ER -

Integral bases and invariant vectors for Weil representations

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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