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Keywords:
restricted Lie superalgebra; $\chi $-reduced representation; indecomposable module; simple module; $p$-character
Summary:
Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type $A(n|0)$, the baby Verma modules $Z_{\chi }(\lambda )$ are proved to be simple for any regular nilpotent $p$-character $\chi $ and typical weight $\lambda $. Moreover, we obtain the dimension formulas for projective covers of simple modules with $p$-characters of standard Levi form.
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