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- Title
Newton-Okounkov convex bodies of Schubert varieties and polyhedral realizations of crystal bases.
- Authors
Fujita, Naoki; Naito, Satoshi
- Abstract
A Newton-Okounkov convex body is a convex body constructed from a projective variety with a valuation on its homogeneous coordinate ring; this is deeply connected with representation theory. For instance, the Littelmann string polytopes and the Feigin-Fourier-Littelmann-Vinberg polytopes are examples of Newton-Okounkov convex bodies. In this paper, we prove that the Newton-Okounkov convex body of a Schubert variety with respect to a specific valuation is identical to the Nakashima-Zelevinsky polyhedral realization of a Demazure crystal. As an application of this result, we show that Kashiwara's involution ( $$*$$ -operation) corresponds to a change of valuations on the rational function field.
- Publication
Mathematische Zeitschrift, 2017, Vol 285, Issue 1/2, p325
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-016-1709-7