Irreducible representations of the classical Lie superalgebra of type $$A(0,n)$$ in prime characteristic
Irreducible representations of the classical Lie superalgebra of type $$A(0,n)$$ in prime characteristic
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DOI：
10.1007/s00605-012-0472-z
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发表时间：
2013-01
期刊：
影响因子：
--
通讯作者：
Yufeng Yao
中科院分区：
文献类型：
--
作者：
Yufeng Yao
设是素特征的代数闭域上的典型李超代数。给出了婴儿Kac-模是单的一个充分条件。此外，还对具有（拟）正则半单特征标的单模进行了分类。特别地，在同构下，确定了的所有单模，并精确地给出了单模的代表和维数。作为应用，对一般线性李超代数的具有某些特征标的单模进行了分类。特别地，给出了简单模的完全分类。
Letbe the classical Lie superalgebra of typeover an algebraically closed field of prime characteristic. A sufficient condition is provided for baby Kac-modules to be simple. Moreover, simple-modules with (quasi) regular semisimple characters are classified. In particular, up to isomorphism, all the simple modules forare determined, and representatives and dimensions of simples are precisely given. As an application, simple modules for the general linear Lie superalgebrawith certain-characters are classified. In particular, a complete classification of simple-modules is given.