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I am currently studying 'advanced' representation theory from a physicist's perspective, including topics like super-Lie algebras. I've come across various gradings (excluding the ℤ2 grading), such as how to select odd roots in Dynkin diagrams, etc., but I couldn't find substantial literature on gradings or any other literature on the representations of graded Lie algebras.

I'm looking for literature that explains and addresses the significance of general gradings and their implications for representation. I've already gone through B. Hall and Fulton & Harris. The only paper that has somewhat helped me is arxiv:1701.03704, where they discuss gradings in relation to Young diagrams. Does anyone have experience with this?

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    $\begingroup$ The first book that comes to mind is the book "Gradings on simple Lie algebras" by Elduque and Kochetov (bookstore.ams.org/surv-189). It doesn't consider Lie superalgebras, though. $\endgroup$
    – Tom De Medts
    Commented Nov 3, 2023 at 17:03

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