Lower Bounds for the Minima of Certain Symplectic and Unitary Group Lattices

Lower Bounds for the Minima of Certain Symplectic and Unitary Group Lattices

We obtain lower bounds for the minimal norms in several families of integral lattices associated to the Weil representations of finite symplectic and unitary groups. Ultimately, these bounds come from Elkies' bounds for a certain family of Wordell-Weil lattices of elliptic curves, and from the...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:American journal of mathematics 1999-08, Vol.121 (4), p.889-918
Hauptverfasser: Dummigan, Neil, Tiep, Pham Huu
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Automorphisms
Conceptual lattices
Crystal lattices
Dot product of vectors
Integers
Mathematical lattices
Mathematical minima
Mathematics
Quaternion algebra
Scalars
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We obtain lower bounds for the minimal norms in several families of integral lattices associated to the Weil representations of finite symplectic and unitary groups. Ultimately, these bounds come from Elkies' bounds for a certain family of Wordell-Weil lattices of elliptic curves, and from the minima of the Barnes-Wall lattices.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.1999.0027