Mathematics – Combinatorics
Scientific paper
2010-08-31
Mathematics
Combinatorics
32 pages, 10 figures
Scientific paper
Schubert varieties in finite dimensional flag manifolds G/P are a well-studied family of projective varieties indexed by elements of the corresponding Weyl group W. In particular, there are many tests for smoothness and rational smoothness of these varieties. One key result due to Lakshmibai-Sandhya is that in type A the smooth Schubert varieties are precisely those that are indexed by permutations that avoid the patterns 4231 and 3412. Recently, there has been a flurry of research related to the infinite dimensional analogs of flag manifolds corresponding with G being a Kac-Moody group and W being an affine Weyl group or parabolic quotient. In this paper we study the case when W is the affine Weyl group of type A or the affine permutations. We develop the notion of pattern avoidance for affine permutations. Our main result is a characterization of the rationally smooth Schubert varieties corresponding to affine permutations in terms of the patterns 4231 and 3412 and the twisted spiral permutations.
Billey Sara
Crites Andrew
No associations
LandOfFree
Pattern characterization of rationally smooth affine Schubert varieties of type A does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Pattern characterization of rationally smooth affine Schubert varieties of type A, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pattern characterization of rationally smooth affine Schubert varieties of type A will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-181109