Irreducible representations of SL(2,C)?

  • Thread starter pellman
  • Start date
  • #1
675
4
The group of SL(2,C) is sometimes defined (by physicists) as the group of 2 X 2 complex matrices of determinant = 1. But then we can talk about other representations of SL(2,C). So apparently the set of 2 X 2 complex matrices of determinant = 1 is but one representation of SL(2,C). If so, what then is the more formal definition of SL(2,C) ? And what does another irreducible representation or SL(2,C) look like?
 

Answers and Replies

  • #2
chiro
Science Advisor
4,790
132
Hey pellman.

I think if you had doubts then you should check the appendix of the document or look for documents that confirm what the definition is across documents and departments.

Usually special groups have unit determinants.
 
  • Like
Likes pellman
  • #3
Stephen Tashi
Science Advisor
7,633
1,492
If we believe the groupprops website, SL(2,C) is defined as the set of matrices that has been mentioned. http://groupprops.subwiki.org/wiki/Special_linear_group:SL(2,C) According to the Wikipedia, you could also defined it as the group of linear transformations on 2-D complex space that preserves oriented areas.
 
  • Like
Likes pellman
  • #4
dextercioby
Science Advisor
Homework Helper
Insights Author
13,033
588
You can define it as the subgroup of GL(2,C) by requiring that the endomorphisms of C2 have a matrix of determinant = 1 in the standard basis of C2.
 
  • Like
Likes pellman
  • #5
675
4
thanks, guys
 

Related Threads on Irreducible representations of SL(2,C)?

Replies
1
Views
3K
Replies
2
Views
5K
Replies
9
Views
3K
  • Last Post
Replies
3
Views
6K
  • Last Post
Replies
1
Views
2K
Replies
14
Views
4K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
636
Replies
3
Views
798
Top