Representations of SU(2) and SO(3)

  • Pr Yvette Kosmann-Schwarzbach
  • Stephanie Frank Singer
Part of the Universitext book series (UTX)


To study the representations of the Lie group SU(2), we first study those of its Lie algebra \({\mathfrak{su}}(2)\), by studying the representations of the Lie algebra \({\mathfrak{sl}}(2, \mathbb{C})\). In fact, by Proposition 1.4 of Chapter 4, if \(\mathfrak{g}^{\mathbb{C}}\) is the complexification of a real Lie algebra \(\mathfrak{g}\), there is a bijective correspondence between irreducible representations of \(\mathfrak{g}\) and of \(\mathfrak{g}^{\mathbb{C}}\). In order to determine the irreducible representations of \({\mathfrak{su}}(2)\), we shall thus study those of \({\mathfrak{sl}}(2, \mathbb{C})\). We recall that by our convention, a representation is a representation on a finite-dimensional complex vector space.


Irreducible Representation Orthonormal Basis Fundamental Representation Homogeneous Polynomial Vector Subspace 
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Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  • Pr Yvette Kosmann-Schwarzbach
    • 1
  • Stephanie Frank Singer
    • 2
  1. 1.Ecole PolytechniquePalaiseauFrance
  2. 2.PhiladelphiaUSA

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