- #1
maverick280857
- 1,789
- 5
Hi,
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!
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!