Decomposition of the Symmetric Powers

Abstract

A decomposition of any symmetric power of ${\mathbb{C}}^2\otimes {\mathbb{C}}^2\otimes {\mathbb{C}}^2$ into irreducible $s{l}_2(\mathbb{C})\oplus s{l}_2(\mathbb{C})\oplus s{l}_2(\mathbb{C})$-submodules are presented. Namely, the multiplicities of irreducible summands in the symmetric power are determined.

arXiv comment13 pages