Affine partitions and affine Grassmannians

Details Affine partitions and affine Grassmannians Affine partitions and affine Grassmannians

2008-03-25

arxiv.org/abs/0803.3647v2

Mathematics

Combinatorics

Scientific paper

We give a bijection between certain colored partitions and the elements in the quotient of an affine Weyl group modulo its Weyl group. By Bott's formula these colored partitions give rise to some partition identities. In certain types, these identities have previously appeared in the work of Bousquet-Melou-Eriksson, Eriksson-Eriksson and Reiner. In other types the identities appear to be new. For type $A_{n}$, the affine colored partitions form another family of combinatorial objects in bijection with $n+1$-core partitions and $n$-bounded partitions. Our main application is to characterize the rationally smooth Schubert varieties in the affine Grassmannians in terms of affine partitions and a generalization of Young's lattice which refines weak order and is a subposet of Bruhat order. Several of the proofs are computer assisted.

Affiliated with

Also associated with

No associations

Rating

Affine partitions and affine Grassmannians 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 Affine partitions and affine Grassmannians, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Affine partitions and affine Grassmannians will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-49425