Folding procedure for Newton-Okounkov polytopes of Schubert varieties |
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Authors: | Naoki Fujita |
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Institution: | Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan |
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Abstract: | The theory of Newton-Okounkov polytopes is a generalization of that of Newton polytopes for toric varieties, and gives a systematic method of constructing toric degenerations of projective varieties. 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, we obtain a new interpretation of Kashiwara’s similarity of crystal bases. |
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Keywords: | Crystal basis fixed point Lie subalgebra Newton-Okounkov body orbit Lie algebra Schubert variety |
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