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Character formulas for restricted simple modules of the special superalgebras. (English) Zbl 1293.17022

Summary: Let \(k\) be an algebraically closed field of prime characteristic \(p > 2\), and let \(S(n)\) be the special Lie superalgebra over \(k\). The iso-classes of simple restricted modules of these algebras are classified, and the character formulas of restricted simple modules are given.

MSC:

17B50 Modular Lie (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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References:

[1] Jacobson, Lie Algebras (1962)
[2] Kac, Lie superalgebras, Adv. Math 26 pp 8– (1977) · Zbl 0366.17012 · doi:10.1016/0001-8708(77)90017-2
[3] Nakano, Projective Modules over Lie Algebras of Cartan Type Vol (1992) · Zbl 0757.17015
[4] Serganova, On representations of Cartan type Lie superalgebras, Am. Math. Soc. Transl 213 pp 223– (2005) · Zbl 1106.17006 · doi:10.1090/trans2/213/14
[5] Shu, Restricted representations of the Witt superalgebras, J. Algebra 324 pp 652– (2010) · Zbl 1217.17010 · doi:10.1016/j.jalgebra.2010.04.032
[6] Zhang, Modular Lie Superalgebras (in Chinese) (2001)
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