Related papers: Supercharacter theories for algebra group extensio…
We construct the supercharacter theory for the finite groups of triangular type. Its special case is the supercharacter theory for algebra groups of P.Diaconis and I.M.Isaacs. The supercharacter analog of the A.A. Kirillov formula for…
We construct two supercharacter theories (in the sense of P. Diaconis and I.M. Isaacs) for the parabolic subgroups in orthogonal and symplectic groups. For each supercharacter theory, we obtain a supercharacter analog of the A.A.Kirillov…
Much can be learned about a finite group from its character table, but sometimes that table can be difficult to compute. Supercharacter theories are generalizations of character theory defined by P. Diaconis and I.M. Isaacs, in which…
The supercharacter theory is constructed for the parabolic subgroups of $\mathrm{GL}(n,\Fq)$ with blocks of orders less or equal to two. The author formulated the hypotheses on construction of a supercharacter theory for an arbitrary…
Diaconis and Isaacs define a supercharacter theory for algebra groups over a finite field by constructing certain unions of conjugacy classes called superclasses and certain reducible characters called supercharacters. This work…
The concept of a supercharacter theory of a finite group was introduced by Diaconis and Isaacs as an alternative to the usual irreducible character theory, and exemplified with a particular construction in the case of finite algebra groups.…
The notion of the supercharacter theory was introduced by P.Diaconis and I.M.Isaaks in 2008. In this paper we review the main statements of the general theory, we observe the construction of supercharacter theory for algebra groups and the…
We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters…
We construct a supercharacter theory for the group of invertible elements of a reduced algebra. For the case of the triangular group, we obtain the formula for values of supercharacters on superclasses.
Supercharacter theory is developed by P. Diaconis and I. M. Isaacs as a natural generalization of the classical ordinary character theory. Some classical sums of number theory appear as supercharacters which are obtained by the action of…
The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of…
We describe the supercharacter theories of the semidirect product of H and K, $H\rtimes K$ in terms of the supercharacter theories of the direct product of H and K in the case when both H and K are Abelian groups. To do this we introduce…
We consider the lattice of supercharacter theories, in the sense of Diaconis and Isaacs, of the cyclic group of order n. We find necessary and sufficient conditions on n for that lattice to be upper or lower semimodular.
We construct supercharacter theories for the finite groups constructed by parabolic constraction from simple groups of $A,B,C,D$ Lie types. In terms of rook placements in the root systems we classify supecharacters and superclasses.
The notion of a supercharacter theory was proposed by P. Diaconis and I.M. Isaacs in 2008. A supercharacter theory for a given finite group is a pair of the system of certain complex characters and the partition of group into classes that…
Diaconis and Isaacs have defined the supercharacter theories of a finite group to be certain approximations to the ordinary character theory of the group. We make explicit the connection between supercharacter theories and Schur rings, and…
There are two main constructions of supercharacter theories for a group $ G $. The first, defined by Diaconis and Isaacs, comes from the action of a group $A$ via automorphisms on our given group $G$. The second, defined by Hendrickson, is…
C. Andre and N. Yan introduced the idea of a supercharacter theory to give a tractable substitute for character theory in wild groups such as the unipotent uppertriangular group $U_n(F_q)$. In this theory superclasses are certain unions of…
We define the superclasses for a classical finite unipotent group $U$ of type $B_{n}(q)$, $C_{n}(q)$, or $D_{n}(q)$, and show that, together with the supercharacters defined in a previous paper, they form a supercharacter theory. In…
The set of supercharacter theories of a fixed group $G$ forms a natural lattice. An open question in the study of supercharacter theories is to classify this lattice, and to date, this has only been done for the cyclic groups…