2010/08/11 by Murray R. Bremner, Bremner, Murray R., Hader A. Elgendy +2
Mathematics · Physics and Astronomy · #17B10 #17B81 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 17A42. Secondary 17A30 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math-ph #math.MP #math.RA #math.RT #msc:17A30 #msc:17A42. #msc:17B10 #msc:17B81
paper · pdf · doi:10.48550/arxiv.1008.1998
26 pages, 13 tables
arxiv created 2010/08/11 · openalex publication_date 2010/08/11 · arxiv updated 2010/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We determine the multiplicity of the irreducible representation V(n) of the\nsimple Lie algebra sl(2,C) as a direct summand of its fourth exterior power\n\Λ4 V(n). The multiplicity is 1 (resp. 2) if and only if n = 4, 6\n(resp. n = 8, 10). For these n we determine the multilinear polynomial\nidentities of degree \≤ 7 satisfied by the sl(2,C)-invariant alternating\nquaternary algebra structures obtained from the projections \Λ4 V(n) \→\nV(n). We represent the polynomial identities as the nullspace of a large\ninteger matrix and use computational linear algebra to find the canonical basis\nof the nullspace.\n