A supercharacter theory for involutive algebra groups.

DOI10.1016/j.jalgebra.2015.02.015zbMath1330.20006arXiv1502.01512OpenAlexW2962781713MaRDI QIDQ2339488

Pedro J. Freitas, Carlos A. M. André, Ana Margarida Neto

Publication date: 1 April 2015

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

Full work available at URL: https://arxiv.org/abs/1502.01512

zbMATH Keywords

Cayley transformsupercharacterssuperclassesfinite unipotent groupsalgebra groups with involution

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15) Representation theory for linear algebraic groups (20G05) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Representations of finite groups of Lie type (20C33)

Related Items (11)

Supercharacters for parabolic contractions of finite groups of 𝐴,𝐵,𝐶,𝐷 Lie types ⋮ A supercharacter theory for Sylow p-subgroups of the Steinberg triality groups ⋮ Irreducible representations of unipotent subgroups of symplectic and unitary groups defined over rings ⋮ Orbit method for \(p\)-Sylow subgroups of finite classical groups ⋮ Supercharacter theories of type \(A\) unipotent radicals and unipotent polytopes ⋮ Supercharacter theories of type \(A\) unipotent radicals and unipotent polytopes ⋮ Supercharacter theories for Sylow \(p\)-subgroups of the Ree groups ⋮ New supercharacter theory for Sylow subgroups in orthogonal and symplectic groups ⋮ Two supercharacter theories for the parabolic subgroups in orthogonal and symplectic groups ⋮ Finding supercharacter theories on character tables ⋮ Supercharacter theories for Sylow p-subgroups of Lie type G₂

Cites Work

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• The antipode and primitive elements in the Hopf monoid of supercharacters
• Irreducible characters of groups associated with finite nilpotent algebras with involution.
• Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs
• A supercharacter theory for the Sylow \(p\)-subgroups of the finite symplectic and orthogonal groups.
• Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
• Super-characters of finite unipotent groups of types \(B_n\), \(C_n\) and \(D_n\).
• Supercharacters of the Sylow \(p\)-subgroups of the finite symplectic and orthogonal groups.
• A super-class walk on upper-triangular matrices
• Basic characters of the unitriangular group
• Characters of groups associated with finite algebras
• Ramanujan sums as supercharacters
• Combinatorial Hopf algebra of superclass functions of type \(D\).
• Basic characters of the unitriangular group (for arbitrary primes)
• A SUPERCHARACTER TABLE DECOMPOSITION VIA POWER-SUM SYMMETRIC FUNCTIONS
• Supercharacters of the adjoint group of a finite radical ring
• Hecke algebras for the basic characters of the unitriangular group
• Supercharacter Theory Constructions Corresponding to Schur Ring Products
• Supercharacters and superclasses for algebra groups
• The basic character table of the unitriangular group

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