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arXiv · 1707.03773

Frobenius splitting of thick flag manifolds of Kac-Moody algebras

Syu Kato
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Abstract

We explain that the Pl\"ucker relations provide the defining equations of the thick flag manifold associated to a Kac-Moody algebra. This naturally transplant the result of Kumar-Mathieu-Schwede about the Frobenius splitting of thin flag manifolds to the thick case. As a consequence, we provide a description of the global sections of line bundles of a thick Schubert variety as conjectured in Kashiwara-Shimozono [Duke Math. J. 148 (2009)]. This also yields the existence of a compatible basis of thick Demazure modules, and the projective normality of the thick Schubert varieties.

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Syu Kato. 2017-07-12. Frobenius splitting of thick flag manifolds of Kac-Moody algebras. https://arxiv.org/abs/1707.03773

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