Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry

Details Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry

2009-02-12

arxiv.org/abs/0902.2181v1

Mathematics

Combinatorics

5 pages, AMS Latex

Scientific paper

We prove that the standard Poisson structure on the Grassmannian Gr(k, n) is invariant under the action of the Coxeter element c =(1 2 ... n). In particular, its symplectic foliation is invariant under c. As a corollary, we obtain a second, Poisson geometric proof of the result of Knutson, Lam, and Speyer that the Coxeter element c interchanges the Lusztig strata of Gr(k, n). We also relate the main result to known anti-invariance properties of the standard Poisson structures on cominuscule flag varieties.

Affiliated with

Also associated with

No associations

Rating

Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry 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 Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cyclicity of Lusztig's stratification of Grassmannians and Poisson geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-556938