Lucas Fresse ; Salah Mehdi - Matrix formulas for multiplicities in the spin module

cm:11156 - Communications in Mathematics, August 27, 2023, Volume 32 (2024), Issue 1 - https://doi.org/10.46298/cm.11156
Matrix formulas for multiplicities in the spin moduleArticle

Authors: Lucas Fresse ; Salah Mehdi

    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 $\mathfrak{sl}(n,{\mathbb C})$ is emphasized.


    Volume: Volume 32 (2024), Issue 1
    Published on: August 27, 2023
    Accepted on: July 7, 2023
    Submitted on: April 5, 2023
    Keywords: Mathematics - Representation Theory

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