Homomorphisms of the alternating group \({\mathcal A}_5\) into reductive groups.

DOI10.1016/S0021-8693(02)00660-9zbMath1074.20030arXivmath/0202111OpenAlexW2055728794MaRDI QIDQ1868754

George Lusztig

Publication date: 28 April 2003

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

Full work available at URL: https://arxiv.org/abs/math/0202111

zbMATH Keywords

reductive algebraic groupsirreducible representationsalternating group \(A_5\)regular homomorphisms

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Subgroup theorems; subgroup growth (20E07) Representation theory for linear algebraic groups (20G05) Discrete subgroups of Lie groups (22E40) Automorphisms of infinite groups (20E36) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (7)

On conjugacy classes of maximal subgroups of finite simple groups, and a related zeta function. ⋮ On conjugacy of \(\operatorname{Alt}_5\)-subgroups of Borovik subgroup of group \(E_8(q)\) ⋮ Higher-dimensional automorphic Lie algebras ⋮ Embeddings of \(Alt_n\) and its perfect covers for \(n\geq 6\) in exceptional complex Lie groups. ⋮ Hereditary automorphic Lie algebras ⋮ On Non-Generic Finite Subgroups of Exceptional Algebraic Groups ⋮ $E_8$, the most exceptional group

Uses Software

• CHEVIE

Cites Work

• Representations of reductive groups over finite fields
• Conjugacy of \(\text{Alt}_5\) and \(\text{SL}(2,5)\) subgroups of \(E_6(\mathbb{C})\), \(F_4(\mathbb{C})\), and a subgroup of \(\mathbb{E}_8(\mathbb{C})\) of type \(A_2E_6\)
• CHEVIE -- A system for computing and processing generic character tables
• Structure of finite subgroups of simple algebraic groups
• Conjugacy of Alt5 and SL(2,5) subgroups of E7( C)
• Some numerical results on the characters of exceptional Weyl groups
• Characters of Reductive Groups over a Finite Field. (AM-107)
• Conjugacy of 𝐴𝑙𝑡₅ and 𝑆𝐿(2,5) subgroups of 𝐸₈(𝐶)
• Finite simple groups which projectively embed in an exceptional Lie group are classified!
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