Newton-Okounkov polytopes of flag varieties
Abstract
We compute the Newton--Okounkov bodies of line bundles on the complete flag variety of GLn for a geometric valuation coming from a flag of translated Schubert subvarieties. The Schubert subvarieties correspond to the terminal subwords in the decomposition (s1)(s2s1)(s3s2s1)(...)(sn-1...s1) of the longest element in the Weyl group. The resulting Newton--Okounkov bodies coincide with the Feigin--Fourier--Littelmann--Vinberg polytopes in type A.
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