Abstract:
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.
Citation:
A. N. Panov, “Supercharacters of unipotent and solvable groups”, Proceedings of the Seminar on algebra and geometry of the Samara University, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 136, VINITI, Moscow, 2017, 31–55; J. Math. Sci. (N. Y.), 235:6 (2018), 714–739
\Bibitem{Pan17}
\by A.~N.~Panov
\paper Supercharacters of unipotent and solvable groups
\inbook Proceedings of the Seminar on algebra and geometry of the Samara University
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 136
\pages 31--55
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into198}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3808186}
\zmath{https://zbmath.org/?q=an:07001312}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 235
\issue 6
\pages 714--739
\crossref{https://doi.org/10.1007/s10958-018-4090-8}
Linking options:
https://www.mathnet.ru/eng/into198
https://www.mathnet.ru/eng/into/v136/p31
This publication is cited in the following 3 articles:
A. N. Panov, “Supercharacter theory for the borel contraction of the group Gl(n,Fq)Gl(n,Fq)”, Vestn. St. Petersbg. Univ., Math., 7:2 (2020), 162–173
A.N. Panov, “Two supercharacter theories for the parabolic subgroups in orthogonal and symplectic groups”, Journal of Algebra, 539 (2019), 37
A. N. Panov, “New supercharacter theory for Sylow subgroups in orthogonal and symplectic groups”, J. Math. Sci. (N. Y.), 243:4 (2019), 612–623
Citation in format AMSBIB
Contact us: