Simplices in Newton-Okounkov bodies and the Gromov width of coadjoint   orbits
  We give a uniform proof for the conjectured Gromov width of coadjoint orbits of all compact connected simple Lie groups, by analyzing simplices in Newton-Okounkov bodies. 
Xin Fang, Peter Littelmann, Milena Pabiniak
math.SG math.AG