Abstract
This chapter reviews the background material on generalized flag varieties including root systems, Weyl groups, parabolic subgroups, Schubert varieties and some representation theory for semisimple algebraic groups. For more details on root systems and Weyl groups, we recommend Humphrey’s Introduction to Lie Algebras and Representation Theory [70] and Reflection Groups and Coxeter Groups [69]. Other references for this chapter are Bourbaki’s Groupes et Algèbres de Lie, Chapters 4, 5 and 6 [23], Borel’s Linear Algebraic Groups [20], Humphrey’s Linear Algebraic Groups [68], and Jantzen’s Representations of Algebraic Groups [76].
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