Hi,(adsbygoogle = window.adsbygoogle || []).push({});

In chapter 12 of GSW volume 2, the authors remark, "spinors form a representation of SO(n) that does not arise from a representation of GL(2,R)."

What do they mean by this?

More generally, since SO(n) is a subgroup of GL(2,R) won't every representation of GL(2,R) be a representation of SO(n) as well?

I know the Dirac matrices of the spinor representation of SO(n) will have different matrix dimension depending on whether n is even or odd. Is that related?

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Group Theory query based on Green Schwarz Witten volume 2

**Physics Forums | Science Articles, Homework Help, Discussion**