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Matrix generators for Weil representations.

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Τίτλος: Matrix generators for Weil representations.
Συγγραφείς: Korhonen, Mikko1 (AUTHOR) mikko.t.korhonen@tuni.fi
Πηγή: Journal of Algebra. Sep2026, Vol. 701, p124-136. 13p.
Θεματικοί όροι: *Representations of groups (Algebra), *Representation theory, *Symplectic groups, *Matrices (Mathematics), *Finite fields, *Mathematics software
Περίληψη: Let r be an odd prime and F a field containing a primitive r th root of unity. Then for all ℓ ≥ 1 , there is a faithful representation f : Sp 2 ℓ (r) → GL r ℓ (F) called the Weil representation. We provide explicit matrices generating Sp 2 ℓ (r) in GL r ℓ (F) , which we have implemented in Magma. We also describe such generators for the irreducible Weil representations of Sp 2 ℓ (r) , which are of degree (r ℓ ± 1) / 2 and arise as irreducible constituents of the Weil representations. [ABSTRACT FROM AUTHOR]
Βάση Δεδομένων: Academic Search Index
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  Data: Matrix generators for Weil representations.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Algebra%22">Journal of Algebra</searchLink>. Sep2026, Vol. 701, p124-136. 13p.
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  Data: Let r be an odd prime and F a field containing a primitive r th root of unity. Then for all ℓ ≥ 1 , there is a faithful representation f : Sp 2 ℓ (r) → GL r ℓ (F) called the Weil representation. We provide explicit matrices generating Sp 2 ℓ (r) in GL r ℓ (F) , which we have implemented in Magma. We also describe such generators for the irreducible Weil representations of Sp 2 ℓ (r) , which are of degree (r ℓ ± 1) / 2 and arise as irreducible constituents of the Weil representations. [ABSTRACT FROM AUTHOR]
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        Value: 10.1016/j.jalgebra.2026.03.043
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 124
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      – SubjectFull: Representations of groups (Algebra)
        Type: general
      – SubjectFull: Representation theory
        Type: general
      – SubjectFull: Symplectic groups
        Type: general
      – SubjectFull: Matrices (Mathematics)
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      – SubjectFull: Finite fields
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      – SubjectFull: Mathematics software
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      – TitleFull: Matrix generators for Weil representations.
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            – D: 01
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
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              Value: 701
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            – TitleFull: Journal of Algebra
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