Modular representations of exceptional supergroups

Modular representations of exceptional supergroups 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., [4]), and they include 3 exceptional Lie superalgebras: D(2|1; ζ), G(3) and F (3|1); cf. [7]. The classification of finite-dimensional simple modules of complex simple Lie superalgebras was achieved by Kac ([10], 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 chengsj@gate.sinica.edu.tw Bin Shu bshu@math.ecnu.edu.cn Weiqiang http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Modular representations of exceptional supergroups

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
D.O.I.
10.1007/s00209-018-2098-x
Publisher site
See Article on Publisher Site

Abstract

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., [4]), and they include 3 exceptional Lie superalgebras: D(2|1; ζ), G(3) and F (3|1); cf. [7]. The classification of finite-dimensional simple modules of complex simple Lie superalgebras was achieved by Kac ([10], 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 chengsj@gate.sinica.edu.tw Bin Shu bshu@math.ecnu.edu.cn Weiqiang

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jun 6, 2018

References

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