Gromov width of non-regular coadjoint orbits of U(n), SO(2n) and SO(2n+1)

2013/02/28 by Milena Pabiniak, Pabiniak, Milena
Mathematics · #53D99 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53D99

paper · pdf · doi:10.48550/arxiv.1302.7213

23 pages, 14 figures

arxiv created 2013/02/28 · arxiv updated 2013/03/01

Abstract

Let G be a compact connected Lie group G and T its maximal torus. The coadjoint orbit O_lambda through lambda in Lie(T)^* is canonically a symplectic manifold. Therefore we can ask the question about its Gromov width. In many known cases the Gromov width is exactly the minimum over the set < alpha_j^\vee,lambda > ; alpha_j^\vee a coroot and < alpha_j^\vee,lambda > positive. We show that the Gromov width of coadjoint orbits of the unitary group and of most of the coadjoint orbits of the special orthogonal group is at least the above minimum. The proof uses the torus action coming from the Gelfand-Tsetlin system.

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