Geodesic
Supercharacters of unipotent and solvable groups
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on algebra and geometry of the Samara University, Tome 136 (2017), pp. 31-55

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The notion of the supercharacter theory was introduced by P. Diaconis and I. M. Isaaks in 2008. In this paper, we review the main notions and facts of the general theory and discuss the construction of the supercharacter theory for algebra groups and the theory of basic characters for unitriangular groups over a finite field. Based on his papers, the author constructs the supercharacter theory for finite groups of triangular type. The structure of the Hopf algebra of supercharacters for triangular groups over finite fields is also characterized.
Keywords: group representations, supercharacter theory, superclasses, Hopf algebra, orbit method. 
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     title = {Supercharacters of unipotent and solvable  groups},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {31--55},
     publisher = {mathdoc},
     volume = {136},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_136_a1/}
}
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A. N. Panov. Supercharacters of unipotent and solvable  groups. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on algebra and geometry of the Samara University, Tome 136 (2017), pp. 31-55. http://geodesic.mathdoc.fr/item/INTO_2017_136_a1/