  Matrix descriptions of even dimensional fuzzy spherical branes $S^{2k} $ in
Matrix Theory and other contexts in Type II superstring theory reveal, in the
large $N$ limit, higher dimensional geometries $SO(2k+1)/U(k)$, which have an
interesting spectrum of $SO(2k+1)$ harmonics and can be up to 20 dimensional,
while the spheres are restricted to be of dimension less than 10. In the case
$k=2$, the matrix description has two dual field theory formulations. One
involves a field theory living on the non-commutative coset $SO(5)/U(2)$ which
is a fuzzy $S^2$ fibre bundle over a fuzzy $S^4$. In the other, there is a U(n)
gauge theory on a fuzzy $S^4$ with $ {\cal O}(n^3)$ instantons. The two
descriptions can be related by exploiting the usual relation between the fuzzy
two-sphere and U(n) Lie algebra. We discuss the analogous phenomena in the
higher dimensional cases, developing a relation between fuzzy $SO(2k)/U(k)$
cosets and unitary Lie algebras.
