.    .			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
.    .			\[ \alpha = \alpha(r,s) =
.    .				\cos(\pi r) + i \sin(\pi r)\cos(\pi s) \]
.    .			\[ \beta = \beta(r,s) = i \sin(\pi r)\sin(\pi s) \]