Irreducible representations of SL(2,C)?

[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?

 

[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.

 

[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.

 

[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.

 

[pellman]

thanks, guys