# Irreducible representations of SL(2,C)?

1. Dec 13, 2014

### pellman

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?

2. Dec 16, 2014

### chiro

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.

3. Dec 16, 2014

### Stephen Tashi

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.

4. Dec 16, 2014

### dextercioby

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.

5. Dec 16, 2014

thanks, guys