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Abstract: Schubert varieties in finite dimensional flag manifolds G-P are awell-studied family of projective varieties indexed by elements of thecorresponding Weyl group W. In particular, there are many tests for smoothnessand rational smoothness of these varieties. One key result due toLakshmibai-Sandhya is that in type A the smooth Schubert varieties areprecisely those that are indexed by permutations that avoid the patterns 4231and 3412. Recently, there has been a flurry of research related to the infinitedimensional analogs of flag manifolds corresponding with G being a Kac-Moodygroup and W being an affine Weyl group or parabolic quotient. In this paper westudy the case when W is the affine Weyl group of type A or the affinepermutations. We develop the notion of pattern avoidance for affinepermutations. Our main result is a characterization of the rationally smoothSchubert varieties corresponding to affine permutations in terms of thepatterns 4231 and 3412 and the twisted spiral permutations.



Autor: Sara Billey, Andrew Crites

Fuente: https://arxiv.org/







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