Constructing the Generators of SU(8) Group in String Theory

[robousy]

Hey folks,

Anyone have any idea where I might find the generators of the SU(8) group, or how I might construct them??

Thanks!

 

[CompuChip]

You could try this page as a starting point... if IIRC the structure constants are just the Levi-Civita tensor (up to a factor plus or minus i ) so you could easily construct them in - for example - the adjoint representation.

But may I ask why on Earth you would want to explicitly construct them?

 

[robousy]

Thanks compuChip. I'm working on a string inspired model building project and I'm trying to find something called a flat direction. My supervisor has me looking at SU(8).

 

[CompuChip]

Hmm, sorry, cannot give you any sensible advise on that.
Let me just point out that, in what I've seen so far of string theory (in particular, and theoretical physics in general) one usually needs to know the algebra and there is no need to explicitly have the elements themselves expressed in some matrix form. So all I can recommend to you is: think carefully if there isn't a way to do the calculation knowing just the commutation relations.

But maybe someone more knowledgeable can give you more sensible ideas