Symplectic Branching through Crystals

2025/05/27 by Bárbara Muniz, Muniz, Bárbara
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2505.21738

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an alternative proof of Naito--Sagaki's conjecture, which states that the restriction of gl_2n(ℂ)-representations to sp_2n(ℂ) can be described in terms of crystals. Using the tableau model for crystals, we construct an explicit and self-contained bijection between their highest weight elements and Sundaram's branching model.

Citations

• A proof of the Naito--Sagaki conjecture via the branching rule for \imathquantum groups
• The branching models of Kwon and Sundaram via flagged hives
• Symplectic tableaux and quantum symmetric pairs
• Combinatorics of generalized exponents
• The honeycomb model of GL(n) tensor products I: proof of the saturation conjecture

Related

• Crystal structure on King tableaux and semistandard oscillating tableaux
• A proof of the Naito--Sagaki conjecture via the branching rule for \imathquantum groups
• On a conjecture by Naito-Sagaki: Littelmann paths and Littlewood-Richardson Sundaram tableaux
• Crystal skeletons: Combinatorics and axioms
• Cocrystals of symplectic Kashiwara-Nakashima tableaux, symplectic Willis like direct way, virtual keys and applications