Titlebook: Classical Lie Algebras at Infinity; Ivan Penkov,Crystal Hoyt Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive li

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Splitting Borel Subalgebras of ,, ,, , and Generalized Flagsebras, since Borel subalgebras are responsible for the very existence of highest weight modules. In this chapter we introduce the special class of splitting Borel subalgebras, and show that their stabilizers are generalized flags.

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Tensor Modules of ,, ,, ,tural and conatural module of .. We will examine the structure of these modules and realize them in a suitable category .. This category is not semisimple, but is Koszul in the sense of Beilinson–Ginzburg–Soergel.

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Weight Modulesheory of weight modules is less developed but is currently coming into shape and will certainly be developed further in the coming years. In this chapter, we give an introduction to weight modules of finite-dimensional Lie algebras, and then we present some basic results on weights modules of root-r

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