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 Mat. Sb. (N.S.), 1985, Volume 128(170), Number 1(9), Pages 21–34 (Mi msb2015)

Irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over a field of positive characteristic

A. N. Panov

Abstract: The irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over an algebraically closed field of characteristic $p>n$ are described. It is proved that an irreducible representation has maximal dimension only if its central character is a nonsingular point of the Zassenhaus manifold.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 56:1, 19–32

Bibliographic databases:

UDC: 512.554
MSC: Primary 17B10; Secondary 17B50, 17B35

Citation: A. N. Panov, “Irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over a field of positive characteristic”, Mat. Sb. (N.S.), 128(170):1(9) (1985), 21–34; Math. USSR-Sb., 56:1 (1987), 19–32

Citation in format AMSBIB
\Bibitem{Pan85} \by A.~N.~Panov \paper Irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over a~field of positive characteristic \jour Mat. Sb. (N.S.) \yr 1985 \vol 128(170) \issue 1(9) \pages 21--34 \mathnet{http://mi.mathnet.ru/msb2015} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=805693} \zmath{https://zbmath.org/?q=an:0603.17008|0585.17009} \transl \jour Math. USSR-Sb. \yr 1987 \vol 56 \issue 1 \pages 19--32 \crossref{https://doi.org/10.1070/SM1987v056n01ABEH003021} 

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This publication is cited in the following articles:
1. A. N. Panov, “Irreducible representations of maximal dimension of simple Lie algrbras over a field of positive characteristic”, Funct. Anal. Appl., 23:3 (1989), 240–241
2. Lev F., “Modular-Representations as a Possible Basis of Finite Physics”, J. Math. Phys., 30:9 (1989), 1985–1998
3. Alexander Premet, “Irreducible representations of Lie algebras of reductive groups and the Kac-Weisfeiler conjecture”, Invent math, 121:1 (1995), 79
4. K.A. Brown, K.R. Goodearl, “Homological Aspects of Noetherian PI Hopf Algebras and Irreducible Modules of Maximal Dimension”, Journal of Algebra, 198:1 (1997), 240
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