Branching polytopes for classical Lie algebras over A_n-1

2020/12/04 by Daniel Kalmbach, Kalmbach, Daniel
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.2012.02883

arxiv created 2020/12/04 · openalex publication_date 2020/12/04 · arxiv updated 2020/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the branching of Lie algebras of classical type over A_n-1 using an inductive approach, which was motivated by the work of Gornitskii. This allows us to label the highest weight vectors of the modules occurring in the decomposition of the restriction of a finite-dimensional simple module to A_n-1 by lattice points of a string or a Lusztig polytope.

Related

• On a property of branching coefficients for affine Lie algebras
• KLR algebras and the branching rule II: the categorical Gelfand-Tsetlin basis for the classical Lie algebras
• Combinatorics of canonical bases revisited: Type A
• A recursion formula for Branching from \mathfraksl_n to \mathfraksl₂ subalgebras
• Branching algebras for the general linear Lie superalgebra