Character sheaves. V

DOI10.1016/0001-8708(86)90071-XzbMath0602.20036MaRDI QIDQ1081701

George Lusztig

Publication date: 1986

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

characteristic functionsintersection cohomologyclass functionscharacter sheavesunipotent classconnected reductive algebraic groupmultiplicity formulairreducible perverse sheaves

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) (p)-adic cohomology, crystalline cohomology (14F30) Cohomology theory for linear algebraic groups (20G10) Other algebraic groups (geometric aspects) (14L40)

Related Items (73)

On total Springer representations for classical types ⋮ Generalized Springer theory for \(D\)-modules on a reductive Lie algebra ⋮ Proof of the Deligne-Langlands conjecture for Hecke algebras ⋮ Minimal idempotents on solvable groups ⋮ The character table of \(\operatorname{GL}_{\mathrm{n}}( \mathbb{F}_{\mathrm{q}}) \rtimes < \sigma >\) ⋮ On the values of unipotent characters of finite Chevalley groups of type \(E_7\) in characteristic 2 ⋮ Correspondance de Langlands géométrique pour les corps de fonctions. (Geometric Langlands correspondence for function fields) ⋮ A formula for the geometric Jacquet functor and its character sheaf analogue ⋮ Rational rigidity for ⋮ Elliptic scalar product. ⋮ Modular generalized Springer correspondence. III: Exceptional groups ⋮ On the involution fixity of exceptional groups of Lie type ⋮ Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution ⋮ Character sheaves on the semi-stable locus of a group compactification. ⋮ Enhanced variety of higher level and Kostka functions associated to complex reflection groups ⋮ Geometric Satake, Springer correspondence and small representations ⋮ Topological generation of exceptional algebraic groups ⋮ Generalized Green functions associated to complex reflection groups ⋮ Formulae for two-variable Green functions ⋮ 𝐙/𝐦-graded Lie algebras and perverse sheaves, II ⋮ On the generalised Springer correspondence for groups of type 𝐸₈ ⋮ Study of parity sheaves arising from graded Lie algebras ⋮ On soluble subgroups of sporadic groups ⋮ Computing Green functions in small characteristic ⋮ Characters of Springer representations on elliptic conjugacy classes ⋮ Green functions and Glauberman degree-divisibility ⋮ The character table of the finite Chevalley group \(F_4(q)\) for \(q\) a power of \(2\) ⋮ Unipotent character sheaves and strata of a reductive group ⋮ On total Springer representations for the symplectic Lie algebra in characteristic 2 and the exotic case ⋮ ENDOSCOPY FOR HECKE CATEGORIES, CHARACTER SHEAVES AND REPRESENTATIONS ⋮ Character sheaves for graded Lie algebras: stable gradings ⋮ An informal introduction to categorical representation theory and the local geometric Langlands program ⋮ Character \(D\)-modules via Drinfeld center of Harish-Chandra bimodules. ⋮ Unitriangular shape of decomposition matrices of unipotent blocks ⋮ 𝐙/𝐦-graded Lie algebras and perverse sheaves, IV ⋮ On orbits in double flag varieties for symmetric pairs ⋮ Exterior powers of the reflection representation in Springer theory ⋮ The geometry of Markov traces. ⋮ Quasisplit Hecke algebras and symmetric spaces. ⋮ Some infinite dimensional representations of reductive groups with Frobenius maps. ⋮ Characteristic cycles for the loop Grassmannian and nilpotent orbits. ⋮ Orbit closures in the enhanced nilpotent cone ⋮ On Lusztig's conjecture for connected and disconnected exceptional groups. ⋮ Springer correspondences for dihedral groups. ⋮ On the Betti numbers of Springer fibers for classical types ⋮ Constructible sheaves on nilpotent cones in rather good characteristic ⋮ Character sheaves on certain spherical varieties. ⋮ Categorification of (induced) cell modules and the rough structure of generalised Verma modules ⋮ A unipotent support for irreducible representations ⋮ Counting conjugacy classes in symmetric spaces over \(\mathbb{F}_q\) ⋮ A remark on cuspidal local systems. ⋮ Generalized Springer correspondence and Green functions for type \(B/C\) graded Hecke algebras. ⋮ Localization of character sheaves. ⋮ Green functions associated to complex reflection groups ⋮ Modular generalized Springer correspondence. I: The general linear group ⋮ On Special Pieces in the Unipotent Variety ⋮ On base sizes for almost simple primitive groups ⋮ Green polynomials of Weyl groups, elliptic pairings, and the extended Dirac index ⋮ A first guide to the character theory of finite groups of Lie type ⋮ Characterizations of character sheaves for complex reductive algebraic groups ⋮ A computation of green functions for some classical groups ⋮ Euler characteristic of Springer fibers ⋮ On the values of unipotent characters in bad characteristic ⋮ On the values of unipotent characters of finite Chevalley groups of type \(E_6\) in characteristic 3 ⋮ On induction of class functions ⋮ Springer basic sets and modular Springer correspondence for classical types ⋮ Propriétés de maximalité concernant une représentation définie par Lusztig ⋮ Commutative character sheaves and geometric types for supercuspidal representations ⋮ Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups ⋮ Rationality properties of unipotent representations. ⋮ GENERALIZED GREEN FUNCTIONS AND UNIPOTENT CLASSES FOR FINITE REDUCTIVE GROUPS, III ⋮ The space of unipotently supported class functions on a finite reductive group. ⋮ Fourier transforms and Frobenius eigenvalues for finite Coxeter groups.

Cites Work

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• On the Green polynomials of classical groups
• Green functions of finite Chevalley groups of type \(E_ n (n=6,7,8)\)
• Intersection cohomology complexes on a reductive group
• Character sheaves. I
• Character sheaves. II
• Character sheaves. III
• Character sheaves. IV
• Green polynomials and singularities of unipotent classes
• Irreducible representations of finite classical groups
• Trigonometric sums, Green functions of finite groups and representations of Weyl groups
• Correction to "On the springer representations op the weyl groups of classical algebraic 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)

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