Abstract
Let \(\mathcal{G}\) be a Kac—Moody group and \({\mathcal{P}_Y} \subset \mathcal{G}\) any parabolic subgroup. The aim of Section 7.1 is to realize the homogeneous space \({\mathcal{X}^Y}{\text{: = }}\mathcal{G}{\text{/}}{\mathcal{P}_Y}\) as a projective ind-variety so that the Schubert subvarieties \(\mathcal{X}_Y^w \subset \mathcal{G}{\text{/}}{\mathcal{P}_Y}\) are indeed closed finite-dimensional (projective) irreducible subvarieties. Fix a (dominant integral) weight \(\lambda \in {D_\mathbb{Z}}\) such that, for \(1 \leqslant i \leqslant \ell ,\lambda (\alpha _i^ \vee ) = 0\) 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, V (λ) acquires a \(\mathcal{G}\)-module structure.
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© 2002 Springer Science+Business Media New York
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Kumar, S. (2002). Generalized Flag Varieties of Kac-Moody Groups. In: Kac-Moody Groups, their Flag Varieties and Representation Theory. Progress in Mathematics, vol 204. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0105-2_7
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DOI: https://doi.org/10.1007/978-1-4612-0105-2_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6614-3
Online ISBN: 978-1-4612-0105-2
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