Unitary Kloosterman sums and the Gelfand-Graev representation of \(GL_2\)

DOI10.1006/jabr.1998.7807zbMath1024.11077OpenAlexW1976369388MaRDI QIDQ1305043

Charles W. Curtis, Ken-ichi Shinoda

Publication date: 27 November 2003

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7807

zbMATH Keywords

Gauss sumsrepresentation theoryKloosterman sumsHecke algebra\(L\)-seriesgeneralized Kloosterman sumsconnected reductive algebraic groupnorm mapfinite field extensionsGelfand-Graev representationEuler product expansionsDavenport-Hasse relationirreducible representations of classical groups

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Gauss and Kloosterman sums; generalizations (11L05) Other character sums and Gauss sums (11T24) Representations of finite groups of Lie type (20C33)

Related Items (8)

A note on the moments of Kloosterman sums ⋮ Infinite families of optimal systems of biangular lines related to representations of \(\mathrm{SL}(2, \mathbb{F}_q)\) ⋮ On values of the Bessel function for generic representations of finite general linear groups ⋮ Notes on the norm map between the Hecke algebras of the Gelfand-Graev representations of \(\text{GL}(2,q^2)\) and \(\text{U}(2,q)\). ⋮ Unipotent Hecke algebras of \(\text{GL}_n(\mathbb{F}_q)\). ⋮ Traces of powers of matrices over finite fields ⋮ Finite Euclidean graphs and Ramanujan graphs ⋮ A skein-like multiplication algorithm for unipotent Hecke algebras

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• Cuspidal Matrix Representations for GL₂ (q ) and GL₃ (q )
• Decomposition of gelfand-graev characters of gl₃(q)
• Kloosterman sums and finite field extensions

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