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

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.

37 pages, 7 figures

References in corpus (1)

• Lower bounds for Gromov width of coadjoint orbits in U(n)

Cited by in corpus (1)

• Lagrangian fibers of Gelfand--Cetlin systems of $\mathrm{SO}(n)$-type