Newton-Okounkov polytopes of type $A$ flag varieties of small ranks arising from cluster structures

Author:

Yunhyung Cho, Naoki Fujita, Akihiro Higashitani, Eunjeong Lee

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Combinatorics (math.CO), Representation Theory (math.RT)

journal:

date:

2023-10-09 16:00:00

Abstract

A flag variety is a smooth projective homogeneous variety. In this paper, we study Newton-Okounkov polytopes of the flag variety $Fl(\mathbb{C}^4)$ arising from its cluster structure. More precisely, we present defining inequalities of such Newton-Okounkov polytopes of $Fl(\mathbb{C}^4)$. Moreover, we classify these polytopes, establishing their equivalence under unimodular transformations.

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