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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.28634 |
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Table of Contents:
- We introduce a one-skeleton path model for Mirkovic-Vilonen polytopes in type A_n. We prove that the Minkowski sum of (MV) polytopes corresponds to the concatenation of one-skeleton paths of this model. We show that MV polytopes induced by fundamental one-skeleton paths are Harder-Narasimhan polytopes. The paths given by an orientation of the fundamental alcove parameterize precisely the cluster variables in the initial seed of the coordinate ring C[N]. We also establish a correspondence between fundamental one-skeleton paths and folded galleries representing maximal faces of subword complexes. Under this correspondence, the comultiplication structure of C[N] matches the intrinsic comultiplication structure of folded galleries given by projections to sub-Coxeter complexes.