Irreducible Representations of so(4,C)

  • Context: Graduate 
  • Thread starter Thread starter aziz113
  • Start date Start date
  • Tags Tags
    Representations
Click For Summary
SUMMARY

The classification of finite-dimensional irreducible representations of so(4,C) is directly linked to the irreducible representations of sl(2,C), as so(4,C) is isomorphic to sl(2,C) × sl(2,C). The representations can indeed be constructed using tensor products of sl(2,C) modules. For a comprehensive exploration of this topic, refer to "Representation Theory" by Fulton and Harris, which provides detailed insights into the representations of so(4,C) and so(n,C) for n<8.

PREREQUISITES
  • Understanding of finite-dimensional representations
  • Familiarity with Lie algebras, specifically so(4,C) and sl(2,C)
  • Knowledge of tensor products in the context of module theory
  • Basic concepts from representation theory as outlined in Fulton and Harris's work
NEXT STEPS
  • Study the tensor product of sl(2,C) modules in detail
  • Read "Representation Theory" by Fulton and Harris for foundational concepts
  • Explore the representation theory of so(n,C) for n<8
  • Investigate the implications of the isomorphism so(4,C) ≅ sl(2,C) × sl(2,C)
USEFUL FOR

Mathematicians, physicists, and students specializing in representation theory, particularly those focused on Lie algebras and their applications in theoretical physics.

aziz113
Messages
6
Reaction score
0
Does anyone know how to classify the finite-dimensional irreducible representations of so(4,C)? Can they all be built from irreducible reps of sl(2,C) given the fact that so(4,C) \cong sl(2,C) \times sl(2,C).

Thanks!
 
Physics news on Phys.org
It depends on what you mean by "built from"!

For an explicit discussion of the representations of so(4,C) (and IIRC so(n,C) for n<8) see Fulton and Harris's Representation Theory.
 
Thanks morphism.

By "build from" I meant taking a tensor product of sl(2,C) modules.

I'll give Fulton and Harris another look.

Thanks again.
 

Similar threads

Undergrad The Lie algebra of ##\frak{so}(3)## without complexification
  • · Replies 2 ·
Replies
2
Views
3K
Graduate The colorful world of ##2\times 2## complex matrices
  • · Replies 22 ·
Replies
22
Views
4K
Graduate Irreducible representations of SL(2,C)?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Getting new irreducible representations from old ones
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Decomposition into irreps of compact Lie group
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Understanding 4-Vector Representations in the Lorentz Group
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
  • · Replies 48 ·
2
Replies
48
Views
6K
Undergrad Proving SL_2(C) Homeomorphic to SU(2)xT & Simple Connectedness
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Does an irreducible representation acting on operators imply....
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Representations of finite groups: Irreducible and reducible
  • · Replies 1 ·
Replies
1
Views
2K