Some history
We have the map
given by
vn(r,s) =
where
We have the map $ b_n: \Sigma^2U(n) \rightarrow SU(n+1) $ \newline given by \[ b_n(g, r, s) = \left[ i(g), v_n(r, s) \right] \] where $i(g)$ is the inclusion, $\left[g, h\right] = ghg^{-1}h^{-1}$ \newline and $ v_n(r,s) = $ \[ \left[ \begin{array}{cccccc} \alpha & 0 & 0 & \cdots & 0 & \beta (-\overline{\alpha})^0 \\ \beta (-\overline{\alpha})^0\overline{\beta} & \alpha & 0 & \cdots & 0 & \beta (-\overline{\alpha})^1 \\ \beta (-\overline{\alpha})^1\overline{\beta} & \beta (-\overline{\alpha})^0\overline{\beta} & \alpha & \cdots & 0 & \beta (-\overline{\alpha})^2 \\ \vdots & \vdots & \vdots & & \vdots & \vdots \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ \vdots & \vdots & \vdots & & \vdots & \vdots \\ \beta (-\overline{\alpha})^{n-1}\overline{\beta} & \beta (-\overline{\alpha})^{n-2}\overline{\beta} & \cdots & \cdots & \alpha & \beta (-\overline{\alpha})^n \\ -(-\overline{\alpha})^n\overline{\beta} & -(-\overline{\alpha})^{n-1}\overline{\beta} & \cdots & \cdots & -(-\overline{\alpha})^0 \overline{\beta} & -(-\overline{\alpha})^n \\ \end{array} \right] \] where \[ \alpha = \alpha(r,s) = \cos(\pi r) + i \sin(\pi r)\cos(\pi s) \] \[ \beta = \beta(r,s) = i \sin(\pi r)\sin(\pi s) \]
What's wrong in computing today
The intelligent mathematical assistant