A super-class walk on upper-triangular matrices

By Ery Arias-Castro, Persi Diaconis, Richard P. Stanley. 2003

74 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/7094bf88301fd02e2f44f8fd8793e7645a176569

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In Discrete Mathematics and Combinatorics

Citations in the corpus

Super-characters of finite unipotent groups of types B n , C n and D n (2006, background): “Our definition extends the one given previously for the case of the unitriangular group Un(q) (see the papers [1,3] and also [11]; in the first two papers, the super-characters were called basic characters), and is also given in terms of certain subsets of (positive) roots.”
A supercharacter theory for the Sylow p-subgroups of the finite symplectic and orthogonal groups (2008, background): “By definition (see, for example, [4], [7], [11], or [17]), the superclass of Um(q) which contains the element 1 + eD,φ ∈ Um(q) is the subset 1 + VD,φ = {1 + a : a ∈ VD,φ} ⊆ Um(q), and we define the superclass KD,φ of U to be the intersection KD,φ = U ∩ (1 + VD,φ) = {x ∈ U : x − 1 ∈ VD,φ}.”
Supercharacters and superclasses for algebra groups (2007, background): “instance, a random-walk example can be found in [4].”
The Markov chain Monte Carlo revolution (2008, methodology): “The detailed use of this required new formula [4] and leads to an extension of the theory to algebra groups in joint work with Isaacs and Theme [22, 34].”
Supercharacter formulas for pattern groups (2006, methodology): “This program was carried out in [8] for Un(Fq).”
Ramanujan sums as supercharacters (2012, background): “Another application may be found in [7], where the authors use supercharacter theory to study random walks on upper triangular matrices.”
Supercharacter Theory Constructions Corresponding to Schur Ring Products (2012, background): “For the group Un q of upper triangular matrices over the field of size q with all diagonal entries one [2–4, 23], and more generally for groups of the form 1+ where is a nilpotent associative q-algebra [7], a particularly nice supercharacter theory exists which is simple enough to be computed explic”
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras (2010, background): “At the same time, supercharacter theory is rich enough to serve as a substitute for ordinary character theory in some problems [7].”