On the green polynomials of a chevalley group of type f4

DOI10.1080/00927878208822732zbMath0485.20031OpenAlexW1987334771MaRDI QIDQ3944766

Toshiaki Shoji

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1080/00927878208822732

zbMATH Keywords

irreducible representationGreen functionsFrobenius mapLie algebrasnilpotent elementChevalley groupsorthogonality relationsrepresentation of Weyl groupvariety of Borel subgroupsSpringer representationsconnected reductive algebraic groupvirtual charactersstable maximal tori

Mathematics Subject Classification ID

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

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Generalized Gelfand-Graev representations of exceptional simple algebraic groups over a finite field. I, Character sheaves. V, On the character values of finite Chevalley groups at unipotent elements, Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, I, Representations of finite groups, A remark on the orthogonality relations for Green functions, On the Green polynomials of classical groups, A variant of the induction theorem for Springer representations., Green functions for groups of typeE₆andF₄in charateristics 2, Computing Green functions in small characteristic, Exterior powers of the reflection representation in Springer theory, Fourier transforms of nilpotently supported invariant functions on a simple Lie algebra over a finite field, Springer's work on unipotent classes and Weyl group representations, Generalised Burnside rings, G-categories and module categories, On the realization of orbit closures as support varieties, Closures of conjugacy classes in \(G_2\), On unitary unipotent representations of 𝑝-adic groups and affine Hecke algebras with unequal parameters, Perverse coherent sheaves and the geometry of special pieces in the unipotent variety., Green polynomials of Weyl groups, elliptic pairings, and the extended Dirac index, Some problems in computational representation theory, On the endomorphism algebra of generalised Gelfand-Graev representations, On the restriction of Deligne-Lusztig characters, Evaluating characteristic functions of character sheaves at unipotent elements, Matrices for affine Hecke modules, Green functions of finite Chevalley groups of type \(E_ n (n=6,7,8)\), On Springer's representations of Weyl groups containing -1, GENERALIZED GREEN FUNCTIONS AND UNIPOTENT CLASSES FOR FINITE REDUCTIVE GROUPS, III

Cites Work

• On the unipotent characters of the exceptional groups over finite fields
• The fixed point subvarieties of unipotent transformations on generalized flag varieties and the Green functions. Combinatorial and cohomological treatments centering \(GL_ n\).
• Representations of reductive groups over finite fields
• Trigonometric sums, Green functions of finite groups and representations of Weyl groups
• A construction of representations of Weyl groups
• A specialization theorem for certain Weyl group representations and an application to the Green polynomials of unitary groups
• Proof of Springer's hypothesis
• On the springer representations of the weyl groups of classical algebraic groups
• On the springer representations of chevalley groups op type f₄
• On the Green Polynomials of Classical Groups
• Green polynomials op finite classical groups
• Conjugacy Classes in Parabolic Subgroups of Semisimple Algebraic Groups