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<p>To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an <i>N</i>-independent reduction of SU(<i>N</i>) tensor products. To this end, we label each irreducible representation by a pair of Young diagrams, with parts acting on quarks and antiquarks. By combining this with a column-wise multiplication of Young diagrams, we generalize the Littlewood-Richardson rule for the product of two Young diagrams to the product of two Young diagram pairs, achieving a general-<i>N</i> decomposition.</p>

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An N-independent tensor decomposition for SU(N)

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月19日

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  • Stefan Keppeler,
  • Malin Sjodahl,
  • Bernanda Telalovic

摘要

To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an N-independent reduction of SU(N) tensor products. To this end, we label each irreducible representation by a pair of Young diagrams, with parts acting on quarks and antiquarks. By combining this with a column-wise multiplication of Young diagrams, we generalize the Littlewood-Richardson rule for the product of two Young diagrams to the product of two Young diagram pairs, achieving a general-N decomposition.