Clifford algebras and Littlewood-Richardson coefficients

2024/11/18 by Calvert, Kieran, Grizelj, Karmen, Krutov, Andrey +1
#05E05 #14N15 #22E47 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2411.11663

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)× 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 ℂ^N, also known as the Hadamard product.

Related

• Multiplication of polynomials on Hermitian symmetric spaces and Littlewood-Richardson coefficients
• Macdonald polynomials and symmetric functions
• Clifford algebras, symmetric spaces and cohomology rings of Grassmannians
• Explicit Families of Spinor Representations
• The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces