Science China Mathematics

, Volume 56, Issue 2, pp 239–252 | Cite as

Non-restricted representations of simple Lie superalgebras of special type and Hamiltonian type

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Abstract

Let \(\mathbb{F}\) be an algebraically closed field of prime characteristic p > 2, and g be a simple Lie superalgebra of special type or Hamiltonian type over \(\mathbb{F}\). We construct the simple g-modules with non-singular characters of height more than one, and some simple modules with singular characters of height more than five. Furthermore, for the case of special type Lie superalgebras, we also construct a class of simple modules with regular semisimple characters of height one. All those simple modules mentioned above are proved to be reduced Kac modules.

Keywords

restricted Lie superalgebra special Lie superalgebra Hamiltonian Lie superalgebra non-restricted representation singular (non-singular) character 

MSC(2010)

17B10 17B20 17B35 17B50 
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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Maritime UniversityShanghaiChina

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