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

2025/05/28 by Lara Bossinger, Bossinger, Lara, Jacinta Torres +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2505.22127

openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Atoms and charge in type C₂
• Pre-canonical bases on affine Hecke algebras
• Combinatorics of canonical bases revisited: String data in type A
• Atomic decomposition of characters and crystals
• Polyhedral parametrizations of canonical bases & cluster duality
• String cone and Superpotential combinatorics for flag and Schubert varieties in type A
• Toric degenerations of Schubert varieties
• Tensor product multiplicities, canonical bases and totally positive varieties

Cited by

• Structure and geometry of the tableaux algebra

Related

• Combinatorics of canonical bases revisited: String data in type A
• On the interplay of the parametrizations of canonical bases by Lusztig\n and string data
• Atomic decomposition of characters and crystals
• Applications of Crystal Bases to Current Problems in Representation Theory
• On combinatorics of string polytopes in types B and C