Character sheaves. IV
type: Item
instance of: scholarly article
title: Character sheaves. IV
zbMATH Open document ID: 0602.20035
DOI: 10.1016/0001-8708(86)90036-8
author: G. Lusztig
published in: Advances in Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The paper under review is part of a series [see Adv. Math. 56, 193-237 (1985; Zbl 0586.20018); 57, 226-265, 266-315 (1985; Zbl 0586.20019 and Zbl 0594.20031)] devoted to the study of a class \(\hat G\) of irreducible perverse sheaves (called character sheaves) on a connected reductive algebraic group G. The numbering of chapters, sections and references continues that of the previous parts. This paper contains a classification of character sheaves of G assuming that G is almost simple of type A (ch. 18), or some classical group of low rank (ch. 19), or a group of type \(E_ 6\), \(E_ 7\), \(G_ 2\) at least under certain restrictions on char(k) of the ground field k (ch. 20), or a group of type \(E_ 8\), \(F_ 4\) and char(k) is good (ch. 21). It is proved that such G are clean and satisfy the parity condition [see part III Points (13.9.2) and (15.3)] and that the class of character sheaves coincides with the class of admissible complexes [see the author, Invent. Math. 75, 205-272 (1984; Zbl 0547.20032)] and that a multiplicity formula holds rather analogous to the main theorem (Point (4.23)) of the book of the author [Characters of reductive groups over a finite field (Ann. Math. Stud. 107) (1984; Zbl 0556.20033)].
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14L40
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20G10
zbMATH DE Number: 3971045
zbMATH Keywords: irreducible perverse sheaves
zbMATH Keywords: character sheaves
zbMATH Keywords: connected reductive algebraic group
zbMATH Keywords: admissible complexes
zbMATH Keywords: multiplicity formula
reviewed by: Nikolai I. Osetinski
MaRDI profile type: Publication
full work available at URL: 0001-8708(86)90036-8
OpenAlex ID: W4213384407
cites work: Representations of reductive groups over finite fields
cites work: Intersection cohomology complexes on a reductive group
cites work: Character sheaves. I
cites work: Q4217748
cites work: Character sheaves. II
cites work: Coxeter orbits and eigenspaces of Frobenius
cites work: Parabolic character sheaves, III
cites work: Regular elements of semisimple algebraic groups
description: scientific article; zbMATH DE number 3971045