SMALLEST DEGREES OF REPRESENTATIONS OF EXCEPTIONAL GROUPS OF LIE TYPE

DOI10.1081/AGB-100002175zbMath1004.20003MaRDI QIDQ2755376

Frank Lübeck

Publication date: 13 November 2002

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

zbMATH Keywords

algorithmsexceptional groups of Lie typeirreducible characterscomplex representationsprojective representationsfinite Chevalley groupssmallest degrees

Mathematics Subject Classification ID

Related Items (32)

Real characters and degrees. ⋮ Unnamed Item ⋮ Brauer's height zero conjecture for the 2-blocks of maximal defect ⋮ Finite groups admitting Grassmannian 4-designs ⋮ Surjective word maps and Burnside's \(p^aq^b\) theorem ⋮ On the 2-decomposition numbers of Steinberg's triality groups \(^3D_4(q)\), \(q\) odd. ⋮ An asymptotic for the Hall-Paige conjecture ⋮ Toward a sharp Baer-Suzuki theorem for the \(\pi \)-radical: exceptional groups of small rank ⋮ Permutation Symmetry Determines the Discrete Wigner Function ⋮ On the decomposition numbers of the Ree groups \(^2F_4(q^2)\) in non-defining characteristic. ⋮ Simple exceptional groups of Lie type are determined by their character degrees. ⋮ Alternating and sporadic simple groups are determined by their character degrees. ⋮ Characters and Brauer trees of the covering group of ²𝐸₆(2) ⋮ Primes dividing the degrees of the real characters. ⋮ Representation growth in positive characteristic and conjugacy classes of maximal subgroups. ⋮ Representation of finite groups: conjectures, reductions, and applications. ⋮ Finite groups with minimal 1-PIM. ⋮ Low-Dimensional Complex Characters of the Symplectic and Orthogonal Groups ⋮ Finite groups have more conjugacy classes ⋮ Simple classical groups of Lie type are determined by their character degrees. ⋮ Localization and finite simple groups. ⋮ On the Decomposition Numbers of Steinberg's Triality Groups³D₄(2ⁿ) in Odd Characteristics ⋮ Characterizing finite quasisimple groups by their complex group algebras. ⋮ The density of representation degrees. ⋮ The Ore conjecture. ⋮ On Huppert's conjecture for the Monster and Baby Monster. ⋮ Rational irreducible characters and rational conjugacy classes in finite groups ⋮ Symmetric powers and a problem of Kollár and Larsen. ⋮ A computational approach to the Frobenius–Schur indicators of finite exceptional groups ⋮ Euler characteristic of Springer fibers ⋮ Products of conjugacy classes and fixed point spaces ⋮ Cross characteristic representations of symplectic and unitary groups

Uses Software

• GAP
• CHEVIE

Cites Work

• Unnamed Item
• On the minimal degrees of projective representations of the finite Chevalley groups
• The faithful linear representations of least degree of \(S_n\) and \(A_n\) over a field of odd characteristic
• Representations of reductive groups over finite fields
• Über die Zerlegungszahlen der Suzukigruppen Sz(q)
• On the minimal degrees of projective representations of the finite Chevalley groups. II
• CHEVIE -- A system for computing and processing generic character tables
• Characters of Reductive Groups over a Finite Field. (AM-107)
• Generalized gelfand-graev characters for steinberg's triality groups and their applications
• Minimal characters of the finite classical groups
• Die unipotenten charaktere von ²F₄(q²)
• On a class of doubly transitive groups

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