Even unimodular lattices associated with the Weil representation of the finite symplectic group

DOI10.1016/0021-8693(89)90232-9zbMath0679.20039OpenAlexW2018997051MaRDI QIDQ1822626

Yanyan Li

Publication date: 1989

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(89)90232-9

zbMATH Keywords

irreducible charactersirreducible componentsintegral latticeSchur indicesirreducible Brauer characterinduced characterWeyl representationeven symmetric positive definite unimodular H-invariant formskew symplectic transformations

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05)

Related Items

A Family of Complex Irreducible Characters Possessed by Unitary and Special Unitary Groups Defined over Local Rings ⋮ Some generalizations of the Weil representations of the symplectic and unitary groups ⋮ Symplectic groups, symplectic spreads, codes, and unimodular lattices ⋮ The Weil representation of a unitary group associated to a ramified quadratic extension of a finite local ring. ⋮ Minimal characters of the finite classical groups ⋮ Weil representations via abstract data and Heisenberg groups: a comparison ⋮ Congruences for certain theta series ⋮ Weil representations of the symplectic group ⋮ Weil representations of symplectic groups over non-principal rings. ⋮ Finite groups over arithmetical rings and globally irreducible representations. ⋮ Clifford theory of Weil representations of unitary groups ⋮ Cross characteristic representations of symplectic and unitary groups ⋮ Symplectic group lattices

Cites Work

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• Real representations of the finite orthogonal and symplectic groups of odd characteristic
• Finite groups and even lattices
• Representations of symplectic groups
• Representations of dimensions $(p^n\pm 1)/2$ of the symplectic group of degree $2n$ over a field of characteristic $p$
• ON THE SCHUR INDICES OF REDUCTIVE GROUPS II
• On Integral Representations of Finite Groups
• Some Representations of Classical Groups
• ON THE DEGREES OF CERTAIN GROUP CHARACTERS
• Characters of Solvable and Symplectic Groups