Frobenius Splitting of Thick Flag Manifolds of Kac–Moody Algebras
Syu Kato
Source abstract
Abstract We explain that the Plücker relations provide the defining equations of the thick flag manifold associated to a Kac–Moody algebra. This naturally transplants the result of Kumar–Mathieu–Schwede about the Frobenius splitting of thin flag varieties to the thick case. As a consequence, we provide a description of the space of global sections of a line bundle of a thick Schubert variety as conjectured in Kashiwara–Shimozono [13]. 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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