The Spin(10) grand unification has a symmetry breaking of SO(10), or Spin(10).

In Wikipedia, it says,

"The symmetry breaking of SO(10) is usually done with a combination of (( a $45_H$ OR a $54_H$) AND ((a $16_H$ AND a $\overline{16}_H$) OR (a $126_H$ AND a $\overline{126}_H$)) )."

I suppose that 16 has something to do with the 16 spinor representation of SO(10), and 45 has something to do with ${10 \choose 2} = 45$, while 126 has something to do with $\frac{1}{2}{10 \choose 5} = 126$.

What does 54 stands for in the representation theory?

So what are so special about these number: **16,45,54, and 126** in these models? And their roles in the representation theory?

This post imported from StackExchange Physics at 2020-11-08 17:31 (UTC), posted by SE-user annie marie heart