Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences

DOI10.1007/s40879-023-00620-5arXiv1812.10226MaRDI QIDQ6040518

Takahiro Tsushima, Naoki Imai

Publication date: 17 May 2023

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.10226

zbMATH Keywords

Weil representationLusztig inductionfinite unitary groupHowe correspondence

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Representations of finite groups of Lie type (20C33)

Related Items

On extended Weil representation for finite general linear group and Howe correspondence ⋮ Trace formulae for actions of finite unitary groups on cohomology of Artin-Schreier varieties ⋮ Local Galois representations of Swan conductor one

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fourier transformat, constants of the functional equations and Weil conjecture
• Representations of reductive groups over finite fields
• Cohomologie étale. Seminaire de géométrie algébrique du Bois-Marie SGA 4 1/2 par P. Deligne, avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier
• Weil representations associated to finite fields
• On the finiteness of the number of unipotent classes
• Irreducible representations of finite classical groups
• The characters of the finite unitary groups
• Weil representations of finite classical groups
• On a lemma of Tate-Thompson
• Howe correspondence for reductive groups over finite fields
• Parabolic Deligne-Lusztig varieties
• The geometric Weil representation
• Sur certains groupes d'opérateurs unitaires
• Représentations unitaires des groupes symplectiques. (Unitary representations of symmetric groups.)
• The characters of the finite symplectic group Sp(4,q), q=2\(^f\)
• STABLE MODELS OF LUBIN–TATE CURVES WITH LEVEL THREE
• Weil Representations as Globally Irreducible Representations
• Coxeter Orbits and Modular Representations
• Low-Dimensional Complex Characters of the Symplectic and Orthogonal Groups
• Deligne-Lusztig restriction of a Gelfand-Graev module
• Weil representations and cusp forms on unitary groups
• Corrigendum, Volume 80
• Unipotent Representations and Reductive Dual Pairs over Finite Fields
• Cross characteristic representations of even characteristic symplectic groups
• Minimal characters of the finite classical groups
• The Characters of the Finite Symplectic Group Sp(4,q)
• On the Character of Weil's Representation