Resolutions and Hilbert Series of the Unitary Highest Weight Modules of the Exceptional Groups
نویسندگان
چکیده
We give a sufficient criterion on a highest weight module of a semisimple Lie algebra to admit a resolution in terms of sums of modules induced from a parabolic subalgebra. In particular, we show that all unitary highest weight modules admit such a resolution. As an application of our results we compute (minimal) resolutions and explicit formulas for the Hilbert series of the unitary highest weight modules of the exceptional groups.
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