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.
Citation:
A. N. Panov, “Irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over a field of positive characteristic”, Math. USSR-Sb., 56:1 (1987), 19–32
\Bibitem{Pan85}
\by A.~N.~Panov
\paper Irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over a~field of positive characteristic
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 1
\pages 19--32
\mathnet{http://mi.mathnet.ru/eng/sm2015}
\crossref{https://doi.org/10.1070/SM1987v056n01ABEH003021}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=805693}
\zmath{https://zbmath.org/?q=an:0603.17008|0585.17009}
Linking options:
https://www.mathnet.ru/eng/sm2015
https://doi.org/10.1070/SM1987v056n01ABEH003021
https://www.mathnet.ru/eng/sm/v170/i1/p21
This publication is cited in the following 4 articles:
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
Alexander Premet, “Irreducible representations of Lie algebras of reductive groups and the Kac-Weisfeiler conjecture”, Invent math, 121:1 (1995), 79
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
Lev F., “Modular-Representations as a Possible Basis of Finite Physics”, J. Math. Phys., 30:9 (1989), 1985–1998
Citation in format AMSBIB
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