nLab representation theory of the special unitary group

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Contents

Contents

Idea

The representation theory of the special unitary group.

Properties

Irreps

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)

References

  • 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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