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Clifford algebras and Littlewood-Richardson coefficients (2411.11663v1)
Published 18 Nov 2024 in math.RT
Abstract: We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G/K$. In particular, for $G/K=U(n)/U(k)\times U(n-k)$, 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.