On the Green polynomials of classical groups
From MaRDI portal
Publication:594194
DOI10.1007/BF01394315zbMath0525.20027OpenAlexW2095141903MaRDI QIDQ594194
Publication date: 1983
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/143071
irreducible representationGreen functionsLie algebraFrobenius morphismnilpotent elementmaximal torusconnected reductive groupl-adic cohomologyrepresentation of Weyl grouptop cohomologyvariety of Borel subgroups
Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Cohomology theory for linear algebraic groups (20G10)
Related Items
Generalized Gelfand-Graev representations of exceptional simple algebraic groups over a finite field. I ⋮ On total Springer representations for classical types ⋮ Character sheaves. V ⋮ On the character values of finite Chevalley groups at unipotent elements ⋮ Pieces of nilpotent cones for classical groups ⋮ Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, I ⋮ Proof of the Deligne-Langlands conjecture for Hecke algebras ⋮ The character table of \(\operatorname{GL}_{\mathrm{n}}( \mathbb{F}_{\mathrm{q}}) \rtimes < \sigma >\) ⋮ Representations of finite groups ⋮ On the computation of unipotent characters of finite classical groups ⋮ Elliptic scalar product. ⋮ A variant of the induction theorem for Springer representations. ⋮ Geometric Satake, Springer correspondence and small representations ⋮ Generalized Green functions associated to complex reflection groups ⋮ On characters and formal degrees of discrete series of affine Hecke algebras of classical types. ⋮ Characters of Springer representations on elliptic conjugacy classes ⋮ On total Springer representations for the symplectic Lie algebra in characteristic 2 and the exotic case ⋮ Ordinary and modular characters of \(\mathrm{SU}(3,p)\). ⋮ 𝐙/𝐦-graded Lie algebras and perverse sheaves, IV ⋮ Weyl group \(q\)-Kreweras numbers and cyclic sieving ⋮ Exterior powers of the reflection representation in Springer theory ⋮ Quelques questions sur les intégrales orbitales unipotentes et les algèbres de Hecke ⋮ Springer correspondences for dihedral groups. ⋮ On the Betti numbers of Springer fibers for classical types ⋮ Springer's work on unipotent classes and Weyl group representations ⋮ Induced and simple modules of double affine Hecke algebras. ⋮ Generalized Springer correspondence and Green functions for type \(B/C\) graded Hecke algebras. ⋮ Remarks on Computing Irreducible Characters ⋮ Green functions associated to complex reflection groups ⋮ Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, II ⋮ On unitary unipotent representations of 𝑝-adic groups and affine Hecke algebras with unequal parameters ⋮ Green polynomials of Weyl groups, elliptic pairings, and the extended Dirac index ⋮ Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theory ⋮ Euler characteristic of Springer fibers ⋮ On Frobenius incidence varieties of linear subspaces over finite fields ⋮ 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 ⋮ On Springer's representations of Weyl groups containing -1 ⋮ GENERALIZED GREEN FUNCTIONS AND UNIPOTENT CLASSES FOR FINITE REDUCTIVE GROUPS, III ⋮ The unipotent class functions of non-split finite special orthogonal groups
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Green functions of finite Chevalley groups of type \(E_ n (n=6,7,8)\)
- La conjecture de Weil. II
- The fixed point subvarieties of unipotent transformations on generalized flag varieties and the Green functions. Combinatorial and cohomological treatments centering \(GL_ n\).
- Green polynomials and singularities of unipotent classes
- Classes unipotentes et sous-groupes de Borel
- 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
- On the springer representations of the weyl groups of classical algebraic groups
- On the green polynomials of a chevalley group of type f4
- On the Green Polynomials of Classical Groups
- Green polynomials op finite classical groups