Representation theory of the finite unipotent linear groups

By Ning Yan. 2001

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A supercharacter theory for the Sylow p-subgroups of the finite symplectic and orthogonal groups (2008, unknown): “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}.”
Ramanujan sums as supercharacters (2012, background): “For instance, André developed a successful supercharacter theory for the unipotent matrix groups Un(q) whose representation theories are known to be wild (see also [64, 65]).”
Supercharacter formulas for pattern groups (2006, background): “[18] Yan, N. “Representations of finite unipotent linear groups by the method of clusters,” 2006 preprint.”
Supercharacters and superclasses for algebra groups (2007, background): “We review some of their main results in Appendix A.) In this paper, we generalize Yan’s approach in order to extend the supercharacter theory of Un(F ) to a much larger class of p-groups: algebra groups over a finite field F of characteristic p.”
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras (2010, background): “Supercharacter theory Supercharacters were first studied by André (e.g. [5]) and Yan [40] in relation to UTn(q) in order to find a more tractable way to understand the representation theory of UTn(q).”