Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 136, Pages 31–55 (Mi into198)  
This article is cited in 2 scientific papers (total in 3 papers)

Supercharacters of unipotent and solvable groups

A. N. Panov

Samara National Research University
Full-text PDF (388 kB) Citations (3)
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.
Funding agency Grant number
Russian Science Foundation 16-41-01013
Deutsche Forschungsgemeinschaft 16-41-01013
This work was supported by the grant RSF-DFG 16-41-01013.
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 235, Issue 6, Pages 714–739
DOI: https://doi.org/10.1007/s10958-018-4090-8
Bibliographic databases:
Document Type: Article
UDC: 512.547.2
MSC: 20C05, 20F16
Language: Russian
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
Citation in format AMSBIB
\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}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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