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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 414, Pages 193–241 (Mi znsl5674)  

This article is cited in 7 scientific papers (total in 8 papers)

Unipotent elements of nonprime order in representations of the classical algebraic groups: two big Jordan blocks

I. D. Suprunenko

Institute of Mathematics, National Academy of Sciences of Belarus, Surganova 11, Minsk, 220072, Belarus
Full-text PDF (501 kB) Citations (8)
References:
Abstract: For irreducible rational representations of the classical algebraic groups in characteristic $p>2$ that are not equivalent to a composition of a group morphism and the standard representation, it is proved that usually the image of a unipotent element of order $p^{s+1}>p$ has at least two Jordan blocks of size $>p^s$; all exceptions are indicated explicitly. As a corollary, irreducible rational representations of these groups whose images contain unipotent elements with just one Jordan block of size $>1$ are classified.
Key words and phrases: classical groups, irreducible representations, images of unipotent elements, Jordan blocks.
Received: 25.10.2012
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 199, Issue 3, Pages 350–374
DOI: https://doi.org/10.1007/s10958-014-1863-6
Bibliographic databases:
Document Type: Article
UDC: 512.743.7
Language: English
Citation: I. D. Suprunenko, “Unipotent elements of nonprime order in representations of the classical algebraic groups: two big Jordan blocks”, Problems in the theory of representations of algebras and groups. Part 25, Zap. Nauchn. Sem. POMI, 414, POMI, St. Petersburg, 2013, 193–241; J. Math. Sci. (N. Y.), 199:3 (2014), 350–374
Citation in format AMSBIB
\Bibitem{Sup13}
\by I.~D.~Suprunenko
\paper Unipotent elements of nonprime order in representations of the classical algebraic groups: two big Jordan blocks
\inbook Problems in the theory of representations of algebras and groups. Part~25
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 414
\pages 193--241
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5674}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 199
\issue 3
\pages 350--374
\crossref{https://doi.org/10.1007/s10958-014-1863-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902357283}
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  • https://www.mathnet.ru/eng/znsl/v414/p193
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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