A Sundaram type bijection for SO(3): vacillating tableaux and pairs of\n standard Young tableaux and orthogonal Littlewood-Richardson tableaux

2018/01/11 by Judith Braunsteiner, Braunsteiner, Judith
Mathematics · Physics and Astronomy · #05E10 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1801.03780

openalex publication_date 2018/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on the direct-sum-decomposition of the rth tensor power of the defining\nrepresentation of the special orthogonal group SO(2k+1) one is interested in a\nbijective approach for determining the Frobenius characters of the isotypic\ncomponents. In particular this leads us to a bijection between vacillating\ntableaux and pairs of standard Young tableaux and orthogonal\nLittlewood-Richardson tableaux, which we present for SO(3). Moreover we\nintroduce the descent set of a vacillating tableau. As our bijection preserves\nthis descent set, we also obtain the quasi-symmetric expansion of the Frobenius\ncharacters.\n

Related

• A Sundaram type bijection for SO(2k+1): vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau
• A new tableau model for irreducible polynomial representations of the orthogonal group
• Identities for vacillating tableaux via growth diagrams
• A bijection between Littlewood-Richardson tableaux and rigged configurations
• Symplectic tableaux and quantum symmetric pairs