Math. Z. https://doi.org/10.1007/s00209-018-2098-x Mathematische Zeitschrift 1 2 3 Shun-Jen Cheng · Bin Shu · Weiqiang Wang Received: 20 February 2018 / Accepted: 12 April 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed ﬁeld of prime characteristic. Keywords Exceptional supergroups · Simple modules · Odd reﬂections Mathematics Subject Classiﬁcation Primary 20G05 · 17B25 Introduction Among the simple Lie superalgebras over the complex ﬁeld C, the basic Lie superalgebras distinguish themselves by admitting a non-degenerate super-symmetric even bilinear form (see, e.g., ), and they include 3 exceptional Lie superalgebras: D(2|1; ζ), G(3) and F (3|1); cf. . The classiﬁcation of ﬁnite-dimensional simple modules of complex simple Lie superalgebras was achieved by Kac (, Theorem 8). Note that the simple highest weight modules whose highest weights are dominant integral (with respect to the even subalgebra) are not all ﬁnite dimensional. This is one of several aspects that super representation theory differs from the classical representation theory dramatically. This classiﬁcation theorem of Kac can be reformulated as a classiﬁcation for simple modules over the corresponding supergroups over C. B Shun-Jen Cheng firstname.lastname@example.org Bin Shu email@example.com Weiqiang
Mathematische Zeitschrift – Springer Journals
Published: Jun 6, 2018
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