2024/08/27 by Lara Bossinger, Bossinger, Lara, Jian‐Rong Li +1 · 4 citations
Mathematics · Physics and Astronomy · #13F60 #14M15 #70S15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2408.14956
openalex publication_date 2024/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the homogeneous coordinate rings of partial flag varieties and Grassmannians in their Plücker embeddings and exhibit an embedding of the former into the latter. Both rings are cluster algebras and the embedding respects the cluster algebra structures in the sense that there exists a seed for the Grassmannian that restricts to a seed for the partial flag variety (i.e. it is obtained by freezing and deleting some cluster variables). The motivation for this project stems from the application of cluster algebras in scattering amplitudes: spinor helicity and momentum twistor varieties describe massless scattering without assuming dual conformal symmetry. Both may be obtained from Grassmanninas which model the dual conformal case. They are instances of partial flag varieties and their cluster structures reveal information for the scattering amplitudes. As an application of our main result we exhibit the relation between these cluster algebras.