The characters of Weil representations associated to finite fields

DOI10.1016/0021-8693(80)90123-4zbMath0444.20034OpenAlexW2018821215MaRDI QIDQ1144659

Ken-ichi Shinoda

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1016/0021-8693(80)90123-4

zbMATH Keywords

symplectic groupHeisenberg groupirreducible representationsWeil representationprojective representationsymplectic vector spacedual reductive pairquadratic Gaussian sums

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15) Representation theory for linear algebraic groups (20G05)

Related Items (12)

Commutative Nilpotent Closed Algebras and Weil Representations ⋮ Inductive blockwise Alperin weight condition for type \(\mathsf{B}\) and odd primes ⋮ A Family of Complex Irreducible Characters Possessed by Unitary and Special Unitary Groups Defined over Local Rings ⋮ Representations of finite groups ⋮ Weil representations over finite fields and Shintani lift. ⋮ Stability of the centers of the symplectic group rings \(\mathbb{Z} [S p_{2 n}(q)\)] ⋮ Spectra of \(p\)-elements in the normalizer of an extraspecial linear group ⋮ CHARACTER DEGREE SUMS AND REAL REPRESENTATIONS OF FINITE CLASSICAL GROUPS OF ODD CHARACTERISTIC ⋮ Irreducible characters of \(\mathrm{GSp}(4, q)\) and dimensions of spaces of fixed vectors ⋮ Weil representations of symplectic groups over non-principal rings. ⋮ On a question of Drinfeld on the Weil representation: the finite field case ⋮ The characters of the finite conformal sympletctic group, CSp(4,q)

Cites Work

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• Weil's representations of the symplectic groups over finite fields
• Weil representations associated to finite fields
• Irreducible representations of finite classical groups
• Weil representations of finite classical groups
• On isometries of inner product spaces
• Construction and classification of irreducible representations of special linear group of the second order over a finite field
• A Note on Counting Nilpotent Matrices of Fixed Rank
• On the Green Polynomials of Classical Groups
• Endomorphisms of linear algebraic groups
• On the Character of Weil's Representation
• On the conjugacy classes in the unitary, symplectic and orthogonal groups

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