Understanding SO(10) GUT Representations

[Saschenka]

Hi, all!

I am about to learn how GUTs (specifically SO(10)) work, but I am stuck already at the different representations.

In SO(10) models all particles are in a $\overline{16}$.
Since $\overline{16}$ x $\overline{16}$ = 10 + $\overline{126}$ + 120, one can couple Higgs fields transforming as 10, $\overline{126}$, or 120 to the particles.

My first question would be: What's the difference between a 126 and a $\overline{126}$?

Maybe someone has a good reference to learn this stuff. I am reading "Grand Unified Theories" from Graham G. Ross currently, but there the above question is not answered. Maybe it's too basic... In scientific papers usually nothing at all is explained (from my perspective...).

Thanks a lot for your help!

Sash

 

[chrispb]

126bar is the complex conjugate of the 126 representation.

 

[haushofer]

Try Georgi. Still one of the best texts to read about unification (and Lie algebras in fundamental physics in general). Also, Zee's QFT book has some nice sections about it. :)