Clifford algebras and Littlewood-Richardson coefficients

We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G\mathrm{/}K$. In particular, for $G\mathrm{/}K=U(n)\mathrm{/}U(k)\times U(n-k)$, we obtain a new way of multiplying Schur polynomials, i.e., computing the Littlewood-Richardson coefficients. The corresponding multiplication on the Clifford algebra side is, in a convenient basis given by projections of the spin module, simply the componentwise multiplication of vectors in ${\mathbb{C}}^N$, also known as the Hadamard product.