nLab representation theory of the special unitary group




The representation theory of the special unitary group.



The irreps of SU(n)SU(n) are those polynomial irreps of GL(n,C), hence those irreps of SL(n,)SL(n,\mathbb{C}), which are labeled by partitions/Young diagrams λPart(n)\lambda \in Part(n) with rows(λ)n1rows(\lambda) \leq n - 1.

(e.g. Peluse 14, p. 14))

Dimension of irreps and hook/content

hook length formulahook-content formula
number of standard Young tableauxnumber of semistandard Young tableaux
dimension of irreps of Sym(n)dimension of irreps of SL(n)


  • Shlomo Sternberg, Section 5 of: Group Theory and Physics, Cambridge University Press 1994

  • Sarah Peluse, Irreducible representations of SU(n)SU(n) with prime power degree, Séminaire Lotharingien de Combinatoire 71 (2014), Article B71d (pdf)

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