Alternating quaternary algebra structures on irreducible representations of sl(2,C)

Abstract

We determine the multiplicity of the irreducible representation V(n) of the simple Lie algebra sl(2,C) as a direct summand of its fourth exterior power ${\Lambda }^{4}V(n)$. The multiplicity is 1 (resp. 2) if and only if n = 4, 6 (resp. n = 8, 10). For these n we determine the multilinear polynomial identities of degree $\le 7$ satisfied by the sl(2,C)-invariant alternating quaternary algebra structures obtained from the projections ${\Lambda }^{4}V(n)\to V(n)$. We represent the polynomial identities as the nullspace of a large integer matrix and use computational linear algebra to find the canonical basis of the nullspace.

26 pages, 13 tables

References in corpus (3)

• Modeling Multiple M2's
• One-loop corrections to Bagger-Lambert theory
• Multi-operator brackets acting thrice