Lower bounds for Gromov width in the SO(n) coadjoint orbits

2011/12/31 by Milena Pabiniak, Pabiniak, Milena
Mathematics · #53D99 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53D99

paper · pdf · doi:10.48550/arxiv.1201.0240

37 pages, 7 figures

arxiv created 2011/12/31 · arxiv updated 2012/01/04

Abstract

Let G be a compact connected Lie group G and T its maximal torus. The coadjoint orbit O_λ through λin the dual of the Lie algebra of T, is canonically a symplectic manifold. Therefore we can ask the question of its Gromov width. In many known cases the width is exactly the minimum over the positive results of pairing λwith coroots: min< α_j^\vee,λ> ; α_j^\vee is a coroot and < α_j^\vee,λ> is positive. We will show that the Gromov width for regular coadjoint orbits of the special orthogonal group is at least this minimum. The proof uses the torus action coming from the Gelfand-Tsetlin system.

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