Generalised Jantzen filtration of exceptional Lie superalgebras
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Let g be an exceptional Lie superalgebra, and let p be the maximal parabolic subalgebra which contains the distinguished Borel subalgebra and has a purely even Levi subalgebra. For any parabolic Verma module in the parabolic category Op, it is shown that the Jantzen filtration is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan–Lusztig polynomials. An explicit description of the submodule lattices of the parabolic Verma modules is given, and formulae for characters and dimensions of the finite-dimensional simple modules are obtained.
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