Titlebook: Kac-Moody Groups, their Flag Varieties and Representation Theory; Shrawan Kumar Textbook 2002 Springer Science+Business Media New York 200

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https://doi.org/10.1007/978-1-4612-0105-2algebraic geometry; algebraic topology; cohomology; group theory; homological algebra; homology; linear op

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Generalized Flag Varieties of Kac-Moody Groups,hat the Schubert subvarieties . are indeed closed finite-dimensional (projective) irreducible subvarieties. Fix a (dominant integral) weight . such that, for . iff i∈Y. Such a λ is called Y-regular. Let V (λ) be an integrable highest weight g-module with highest weight λ. From the last chapter, . (λ) acquires a .-module structure.

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978-1-4612-6614-3Springer Science+Business Media New York 2002

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An Introduction to ind-Varieties and pro-Groups,Sections 4.1-4.3 are devoted to developing the basic definitions, examples and elementary properties of ind-varieties and ind-groups introduced by [Šafarevi č82], which is our basic reference.

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BGG and Kempf Resolutions,The aim of this chapter is to obtain the BGG resolution and the dual Kempf resolution in an arbitrary Kac—Moody situation.

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Defining Equations of , and Conjugacy Theorems,Fix a subset Y⊂{1,...,e} and a Y-regular weight Λ ∈ ., i.e., A is dominant totally integral and Λ(α.) iff ∈ Y.