Supercharacter formulas for pattern groups

DOI10.1090/S0002-9947-09-04521-8zbMath1205.20006arXivmath/0610161MaRDI QIDQ3631864

Nathaniel Thiem, Persi Diaconis

Publication date: 22 June 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610161

zbMATH Keywords

posetsunions of conjugacy classessupercharacterssuperclassesalgebra groupspattern groupsfinite unipotent groups

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15)

Related Items (31)

The number of conjugacy classes in pattern groups is not a polynomial function ⋮ Characters of 2-layered Heisenberg groups ⋮ Closed expressions for averages of set partition statistics ⋮ The combinatorics of normal subgroups in the unipotent upper triangular group ⋮ Superinduction for pattern groups. ⋮ Normal supercharacter theories and their supercharacters ⋮ Representations of Unitriangular Groups ⋮ Supercharacters and the discrete Fourier, cosine, and sine transforms ⋮ The Hopf monoid on nonnesting supercharacters of pattern groups ⋮ Combinatorial methods of character enumeration for the unitriangular group. ⋮ An analog of nilpotence arising from supercharacter theory ⋮ Characters arising from monomial coadjoint orbits for finite pattern groups ⋮ A conjecture about characters of finite pattern groups ⋮ Scaling limits for width two partially ordered sets: the incomparability window ⋮ On a supercharacter analog of nilpotent groups ⋮ A supercharacter analogue for normality. ⋮ Superclasses and supercharacters of normal pattern subgroups of the unipotent upper triangular matrix group. ⋮ Exotic characters of unitriangular matrix groups. ⋮ Groups with one or two super-Brauer character theories ⋮ Supercharacters and pattern subgroups in the upper triangular groups ⋮ Supercharacters of unipotent groups defined by involutions. ⋮ Ramanujan sums as supercharacters ⋮ Super-Brauer characters and super-regular classes. ⋮ Branching rules in the ring of superclass functions of unipotent upper-triangular matrices ⋮ \(\operatorname{GL}_n(\mathbb{F}_q)\)-analogues of factorization problems in the symmetric group ⋮ The Markov chain Monte Carlo revolution ⋮ Supercharacter Theories Constructed by the Method of Little Groups ⋮ Heisenberg characters, unitriangular groups, and Fibonacci numbers ⋮ Ограничение и индуцирование суперхарактеров конечных групп треугольного типа ⋮ Characters of unipotent radicals of standard parabolic subgroups with 3 parts ⋮ Super-π-Brauer Characters and Super-π-Regular Classes

Cites Work

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• Super-characters of finite unipotent groups of types \(B_n\), \(C_n\) and \(D_n\).
• Comparison techniques for random walk on finite groups
• Computing in unitriangular matrices over finite fields
• A super-class walk on upper-triangular matrices
• Basic sums of coadjoint orbits of the unitriangular group
• Counting characters of upper triangular groups.
• Basic characters of the unitriangular group (for arbitrary primes)
• Counting conjugacy classes of unitriangular groups associated to finite-dimensional algebras
• Supercharacters and superclasses for algebra groups
• The basic character table of the unitriangular group

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