Abstract
We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.
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Brundan, J.: Modular representations of the supergroup \(Q(n)\), II. Pacific J. Math. 224, 65–90 (2006)
Brundan, J., Kleshchev, A.: Modular representations of the supergroup \(Q(n)\), I. J. Algebra 260, 64–98 (2003)
Brundan, J., Kujawa, J.: A new proof of the Mullineux conjecture. J. Algebraic Combin. 18, 13–39 (2003)
Cheng, S.-J., Wang, W.: Dualities and Representations of Lie Superalgebras, Graduate Studies in Mathematics. Am. Math. Soc. 144 (2012)
Cheng, S.-J., Wang, W.: Character formulae in category \(\cal{O}\) for exceptional Lie superalgebras \(D(2|1;\zeta )\). Transform. Groups (to appear). arXiv:1704.00846v3
Fioresi, R., Gavarini, F.: Chevalley supergroups. Mem. Am. Math. Soc. 215, 1014 (2012)
Freund, P., Kaplansky, I.: Simple supersymmetries. J. Math. Phys. 17, 228–231 (1976)
Gavarini, F.: Chevalley Supergroups of type \(D(2,1;a)\). Proc. Edinb. Math. Soc. 57, 465–491 (2014)
Jantzen, J.C.: Reresentations of Algebraic Groups, 2nd edn. American Mathematical Society, Providence (2003)
Kac, V.: Lie superalgebras. Adv. Math. 16, 8–96 (1977)
Leites, D., Saveliev, M., Serganova, V.: Embedding of \( osp (N/2)\) and the associated non-linear supersymmetric equations. Group theoretical methods in physics, Vol. I (Yurmala: 255–297, p. 1986. Press, Utrecht, VNU Sci) (1985)
Martirosyan, L.: The representation theory of the exceptional Lie superalgebras \(F(4)\) and \(G(3)\). J. Algebra 419, 167–222 (2014)
Masuoka, A.: Harish-Chandra pairs for algebraic affine supergroup schemes over an arbitrary field. Transform. Groups 17, 1085–1121 (2012)
Masuoka, A., Shibata, T.: Algebraic supergroups and Harish-Chandra pairs over a commutative ring. Trans. Am. Math. Soc. 369, 3443–3481 (2017)
Masuoka, A., Zubkov, A.N.: Solvability and nilpotency for algebraic supergroups. J. Pure Appl. Algebra 221, 339–365 (2017)
Serganova, V.: Kac-Moody superalgebras and integrability. Developments and Trends in Infinite-Dimensional Lie Theory. Progr. Math. 288, 169–218 (2011). (Birkhäuser)
Shu, B., Wang, W.: Modular representations of the ortho-symplectic supergroups. Proc. London Math. Soc. 96, 251–271 (2008)
Zubkov, A.N.: On some properties of Noetherian superschemes (Russian), Algebra Logic, to appear
Acknowledgements
S.-J.C. is partially supported by a MoST and an Academia Sinica Investigator grant; B.S. is partially supported by the National Natural Science Foundation of China (Grant Nos. 11671138, 11771279) and Shanghai Key Laboratory of PMMP (No. 13dz2260400); W.W. is partially supported by an NSF Grant DMS-1702254. We thank East China Normal University and Institute of Mathematics at Academia Sinica for hospitality and support.
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Cheng, SJ., Shu, B. & Wang, W. Modular representations of exceptional supergroups. Math. Z. 291, 635–659 (2019). https://doi.org/10.1007/s00209-018-2098-x
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DOI: https://doi.org/10.1007/s00209-018-2098-x