Newton-Okounkov polytopes of flag varieties
arXiv:1506.00362 · doi:10.1007/s00031-016-9372-y
Abstract
We compute the Newton--Okounkov bodies of line bundles on the complete flag variety of GL_n for a geometric valuation coming from a flag of translated Schubert subvarieties. The Schubert subvarieties correspond to the terminal subwords in the decomposition (s_1)(s_2s_1)(s_3s_2s_1)(...)(s_{n-1}...s_1) of the longest element in the Weyl group. The resulting Newton--Okounkov bodies coincide with the Feigin--Fourier--Littelmann--Vinberg polytopes in type A.
16 pages, 2 figures, final version, typos corrected, details added, a new proof (Example 2.9, Remark 2.10) outlined