Meaninig of a symbol at the Circle Group

Question

I have $U_{20}$ (at the meainig of the Circle Group),

What is the meaning of $W_{20}^{8}$??

What is the 20 and what is the 8?

Thank you!

Answer 1

Assuming you mean $W = \omega$, then I suspect $\;\omega^8_{20}\;$ denotes the $8$th root of unity in $U_{20}= \left\{\omega^k_{20} = e^{\large\frac{ik2\pi}{20}}\mid\in \mathbb Z, 1 \leq k \leq 20\right\}$, where $\omega$ denotes the element $e^{\large\frac{2i\pi}{20}} = e^{\large \frac{i\pi}{10}}\in U_{20}$ that generates all of $U_{20}$. So $\omega^8_{20}$ would the element $e^{\large\frac{8i\pi}{10}} = e^{4i\pi/5}$.