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arXiv · 1703.03144

Folding procedure for Newton-Okounkov polytopes of Schubert varieties

Naoki Fujita
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Abstract

The theory of Newton-Okounkov polytopes is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of a projective variety. In the case of Schubert varieties, their Newton-Okounkov polytopes are deeply connected with representation theory. Indeed, Littelmann's string polytopes and Nakashima-Zelevinsky's polyhedral realizations are obtained as Newton-Okounkov polytopes of Schubert varieties. In this paper, we apply the folding procedure to a Newton-Okounkov polytope of a Schubert variety, which relates Newton-Okounkov polytopes of Schubert varieties of different types. As an application of this result, we obtain a new interpretation of Kashiwara's similarity of crystal bases.

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Naoki Fujita. 2017-03-09. Folding procedure for Newton-Okounkov polytopes of Schubert varieties. https://arxiv.org/abs/1703.03144

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