Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions
arXiv:2505.22127
Abstract
We present n-1 different embeddings of string polytopes of type A. We characterize their compatibility with the crystal structure on the string polytopes, and formulate a conjecture describing how to obtain n-1 different atomic decompositions of the crystal with highest weight a multiple of the highest root.
12 pages, comments very welcome!