Matrix formulas for multiplicities in the spin module

DOI10.46298/CM.11156arXiv2304.01699MaRDI QIDQ6509497

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Abstract: We obtain inductive and enumerative formulas for the multiplicities of the weights of the spin module for the Clifford algebra of a Levi subalgebra in a complex semisimple Lie algebra. Our formulas involve only matrices and tableaux, and our techniques combine linear algebra, Lie theory, and combinatorics. Moreover, this suggests a relationship with complex nilpotent orbits. The case of the special linear Lie algebra $mathfraksl(n,mathbbC)$ is emphasized.

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