2017/07/12 by Syu Kato, Kato, Syu
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1707.03773
We explain that the Plücker 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.