Green functions of finite Chevalley groups of type \(E_ n (n=6,7,8)\)

DOI10.1016/0021-8693(84)90084-XzbMath0539.20025MaRDI QIDQ793844

W. M. Beynon, Nicolas Spaltenstein

Publication date: 1984

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

zbMATH Keywords

Zariski closuresGreen functionsFrobenius endomorphismunipotent orbitsconnected reductive algebraic group

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Linear algebraic groups over finite fields (20G40)

Related Items (47)

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 ⋮ Classification of one $\textsf K$-type representations ⋮ Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, I ⋮ Proof of the Deligne-Langlands conjecture for Hecke algebras ⋮ Springer's Weyl group representations through characteristic classes of cone bundles ⋮ Representations of finite groups ⋮ Generic singularities of nilpotent orbit closures ⋮ A remark on the orthogonality relations for Green functions ⋮ On the Green polynomials of classical groups ⋮ Unnamed Item ⋮ A variant of the induction theorem for Springer representations. ⋮ Geometric Satake, Springer correspondence and small representations ⋮ Green functions for groups of typeE₆andF₄in charateristics 2 ⋮ Computing Green functions in small characteristic ⋮ Green functions and Glauberman degree-divisibility ⋮ On the irreducibility of associated varieties of \(W\)-algebras ⋮ Quiver theories and formulae for nilpotent orbits of exceptional algebras ⋮ An effective method to compute closure ordering for nilpotent orbits of \(\theta \)-representations ⋮ 𝐙/𝐦-graded Lie algebras and perverse sheaves, IV ⋮ The closure diagram for nilpotent orbits of the split real form of \(E_8\) ⋮ Exterior powers of the reflection representation in Springer theory ⋮ On the Betti numbers of Springer fibers for classical types ⋮ Springer's work on unipotent classes and Weyl group representations ⋮ Algebraic and analytic Dirac induction for graded affine Hecke algebras ⋮ The closure diagrams for nilpotent orbits of the real forms EVI and EVII of 𝐄₇ ⋮ The closure diagram for nilpotent orbits of the split real form of 𝐸₇ ⋮ Rational points on generalized flag varieties and unipotent conjugacy in finite groups of Lie type ⋮ Remarks on Computing Irreducible Characters ⋮ Closures of conjugacy classes in \(G_2\) ⋮ Unitary ℐ-spherical representations for split 𝓅-adic 𝐄₆ ⋮ 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 ⋮ Unnamed Item ⋮ On Frobenius incidence varieties of linear subspaces over finite fields ⋮ On the values of unipotent characters of finite Chevalley groups of type \(E_6\) in characteristic 3 ⋮ Whittaker unitary dual of affine graded Hecke algebras of type E ⋮ On the endomorphism algebra of generalised Gelfand-Graev representations ⋮ Bases in equivariant 𝐾-theory. II ⋮ Evaluating characteristic functions of character sheaves at unipotent elements ⋮ Green functions of finite Chevalley groups of type \(E_ n (n=6,7,8)\) ⋮ On Springer's representations of Weyl groups containing -1 ⋮ The development version of the \texttt{CHEVIE} package of \texttt{GAP3}. ⋮ GENERALIZED GREEN FUNCTIONS AND UNIPOTENT CLASSES FOR FINITE REDUCTIVE GROUPS, III

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Intersection homology. II
• Green functions of finite Chevalley groups of type \(E_ n (n=6,7,8)\)
• Representations of finite Chevalley groups. A survey
• On the fixed point set of a unipotent element on the variety of Borel subgroups
• The conjugate classes of unipotent elements of the Chevalley groups \(E_ 7\) and \(E_ 8\).
• Green polynomials and singularities of unipotent classes
• Representations of reductive groups over finite fields
• Trigonometric sums, Green functions of finite groups and 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
• The classes and representations of the groups of 27 lines and 28 bitangents
• Some numerical results on the characters of exceptional Weyl groups
• On the green polynomials of a chevalley group of type f₄
• On Springer's correspondence for simple groups of type E_n (n = 6, 7, 8)
• Classes of unipotent elements in simple algebraic groups. II
• Induced Unipotent Classes

This page was built for publication: Green functions of finite Chevalley groups of type \(E_ n (n=6,7,8)\)