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

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

2010-08-11

arxiv.org/abs/1008.1998v1

Mathematics

Rings and Algebras

26 pages, 13 tables

Scientific paper

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.

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