Unitriangular shape of decomposition matrices of unipotent blocks

DOI10.4007/annals.2020.192.2.7zbMath1480.20041arXiv1910.08830OpenAlexW2981240332MaRDI QIDQ2206348

Olivier Brunat, Jay Taylor, Olivier Dudas

Publication date: 22 October 2020

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.08830

zbMATH Keywords

finite groups of Lie typedecomposition numbersgeneralised Gelfand-Graev representations

Mathematics Subject Classification ID

Representations of finite groups of Lie type (20C33)

Related Items (9)

Inductive blockwise Alperin weight condition for type \(\mathsf{B}\) and odd primes ⋮ Alperin weight conjecture and related developments ⋮ Decomposition numbers and global properties ⋮ Jordan decomposition for weights and the blockwise Alperin weight conjecture ⋮ EXTENSIONS OF CHARACTERS IN TYPE D AND THE INDUCTIVE MCKAY CONDITION, I ⋮ Decomposition matrices over unitriangulars ⋮ Unitriangular basic sets, Brauer characters and coprime actions ⋮ Galois automorphisms and classical groups ⋮ On modular Harish-Chandra series of finite unitary groups

Uses Software

• CHEVIE

Cites Work

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• Generic singularities of nilpotent orbit closures
• Stable basic sets for finite special linear and unitary groups
• Derived categories and Deligne-Lusztig varieties. II.
• A reduction theorem for the Alperin weight conjecture.
• Isométries de caractères et équivalences de Morita ou dérivées. (Isometries of characters and Morita or derived equivalences)
• Unipotent classes in maximal subgroups of exceptional algebraic groups.
• Green functions and character sheaves
• On the decomposition numbers of the finite unitary groups in non-defining characteristic
• An introduction to homological algebra
• Unipotent representations of complex semisimple groups
• Character sheaves. III
• Generalized Gelfand-Graev representations of exceptional simple algebraic groups over a finite field. I
• Character sheaves. V
• On the decomposition numbers of \(G_ 2(q)\)
• Classes unipotentes et sous-groupes de Borel
• A unipotent support for irreducible representations
• Weil representations associated to finite fields
• Basic sets of Brauer characters of finite groups of Lie type. III
• Derived categories and Deligne-Lusztig varieties.
• Unipotent elements and generalized exponential maps
• Modular irreducibility of cuspidal unipotent characters
• Decomposition numbers of \(\text{SU}(3,q^2)\)
• Component groups of unipotent centralizers in good characteristic
• Nilpotent orbits in good characteristic and the Kempf-Rousseau theory
• Nilpotent orbits over ground fields of good characteristic
• On the computation of unipotent characters of finite classical groups
• Computing Green functions in small characteristic
• The development version of the \texttt{CHEVIE} package of \texttt{GAP3}.
• Equivariant character correspondences and inductive McKay condition for type \(\mathsf{A}\)
• On unipotent supports of reductive groups with a disconnected centre.
• Optimal \(\text{SL}(2)\)-homomorphisms.
• Families and Springer's correspondence.
• On character sheaves and characters of reductive groups at unipotent classes.
• Groupes reductifs
• Normalisateurs de tores. I: Groupes de Coxeter etendus
• Seminar on algebraic groups and related finite groups. Held at the Institute for Advanced Study, Princeton/N.J., 1968/69
• The automorphism group of an extraspecial \(p\)-group
• On the smoothness of centralizers in reductive groups
• Parity sheaves
• GENERALIZED GELFAND–GRAEV REPRESENTATIONS IN SMALL CHARACTERISTICS
• Decomposition numbers of finite classical groups for linear primes.
• Characters of Reductive Groups over a Finite Field. (AM-107)
• The q ‐Schur Algebra
• On Cocharacters Associated to Nilpotent Elements of Reductive Groups
• Generalized gelfand-graev characters for steinberg's triality groups and their applications
• Basic Sets of Brauer Characters of Finite Groups of Lie Type II
• Character Sheaves and Generalized Gelfand-Graev Characters
• Quasi-semisimple elements
• The Structure of Root Data and Smooth Regular Embeddings of Reductive Groups
• On the existence of a unipotent support for the irreducible characters of a finite group of Lie type
• Computing in groups of Lie type
• Restriction of a character sheaf to conjugacy classes
• Basic Sets for Unipotent Blocks of Finite Reductive Groups in Bad Characteristic
• Remarks on modular representations of finite groups of Lie type in non-defining characteristic
• SUPPORTS UNIPOTENTS DE FAISCEAUX CARACTÈRES
• Lusztig’s conjecture for finite special linear groups
• Endomorphisms of linear algebraic groups
• Linear algebraic groups.
• Ideals in polynomial rings and the module of differentials

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