Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions

Published 28 May 2025 in math.RT and math.CO | (2505.22127v1)

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.

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