Non-restricted representations of simple Lie superalgebras of special type and Hamiltonian type
Let \(\mathbb{F}\) be an algebraically closed field of prime characteristic \(p > 2\), and \(\mathfrak g\) be a simple Lie superalgebra of special type or Hamiltonian type over \(\mathbb{F}\). The author first constructs the simple \(\mathfrak g\)-modules with non-singular characters, and prove the simplicity of the \(\chi\)-reduced Kac modules, where \(\chi\) is a non-singular character of height more than one. The author then constructs some simple modules with singular characters, and proves the simplicity of the \(\chi\)-reduced Kac modules, where \(\chi\) is a singular character of so-called \(\delta\)-invertible type. Furthermore, for the case of special type Lie superalgebras, the author also studies a class of reduced Kac modules with regular semisimple characters of height one, and it is to be simple.
scientific article; zbMATH DE number 6151457
scientific article