Polyhedral realizations of crystal bases and convex-geometric Demazure operators

30 Oct 2018  ·  Fujita Naoki ·

The main object in this paper is a certain rational convex polytope whose lattice points give a polyhedral realization of a highest weight crystal basis. This is also identical to a Newton-Okounkov body of a flag variety, and it gives a toric degeneration... In this paper, we prove that a specific class of this polytope is given by Kiritchenko's Demazure operators on polytopes. This implies that polytopes in this class are all lattice polytopes. As an application, we give a sufficient condition for the corresponding toric variety to be Gorenstein Fano. read more

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Algebraic Geometry Combinatorics Representation Theory