Super-characters of finite unipotent groups of types \(B_n\), \(C_n\) and \(D_n\).

DOI10.1016/j.jalgebra.2006.04.030zbMath1104.20041OpenAlexW1991412466MaRDI QIDQ854907

Carlos A. M. André, Ana Margarida Neto

Publication date: 7 December 2006

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.04.030

zbMATH Keywords

symplectic groupsorthogonal groupsirreducible charactersbasic sets of positive rootsfinite unipotent groupssuper-characters

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05)

Related Items (29)

Superinduction for pattern groups. ⋮ Combinatorics of \(B\)-orbits and Bruhat-Chevalley order on involutions. ⋮ Counting irreducible representations of large degree of the upper triangular groups. ⋮ The Hopf monoid on nonnesting supercharacters of pattern groups ⋮ A \(\mathrm{GL}(\mathbb{F}_q)\)-compatible Hopf algebra of unitriangular class functions ⋮ Restrictions of rainbow supercharacters ⋮ Combinatorial Hopf algebra of superclass functions of type \(D\). ⋮ Characters of the Sylow \(p\)-subgroups of the Chevalley groups \(D_4(p^n)\). ⋮ Supercharacters of the adjoint group of a finite radical ring ⋮ A supercharacter theory for Sylow p-subgroups of the Steinberg triality groups ⋮ Strong forms of linearization for Hopf monoids in species ⋮ Gradedness of the set of rook placements in \(A_{n -1}\) ⋮ Supercharacters and pattern subgroups in the upper triangular groups ⋮ Irreducible representations of unipotent subgroups of symplectic and unitary groups defined over rings ⋮ Nonzero coefficients in restrictions and tensor products of supercharacters of \(U_n(q)\). ⋮ Supercharacters of unipotent groups defined by involutions. ⋮ Orbit method for \(p\)-Sylow subgroups of finite classical groups ⋮ Branching rules in the ring of superclass functions of unipotent upper-triangular matrices ⋮ Supercharacter theories for Sylow \(p\)-subgroups of the Ree groups ⋮ A supercharacter theory for the Sylow \(p\)-subgroups of the finite symplectic and orthogonal groups. ⋮ Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups. ⋮ The Bruhat-Chevalley order on involutions of the hyperoctahedral group and the combinatorics of \(B\)-orbit closures. ⋮ Supercharacter Theories Constructed by the Method of Little Groups ⋮ Irreducible characters of large degree of Sylow \(p\)-subgroups of classical groups. ⋮ Supercharacter formulas for pattern groups ⋮ Orthogonal subsets of root systems and the orbit method ⋮ Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras ⋮ A supercharacter theory for involutive algebra groups. ⋮ Supercharacter theories for Sylow p-subgroups of Lie type G₂

Cites Work

• Proof of Springer's hypothesis
• A super-class walk on upper-triangular matrices
• Basic characters of the unitriangular group
• Basic sums of coadjoint orbits of the unitriangular group
• Basic characters of the unitriangular group (for arbitrary primes)
• Hecke algebras for the basic characters of the unitriangular group
• Uniform convergence and decay of Fourier series on compact nilmanifolds
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