The-Singularity-Research / plethysm

Using plethysm to compute the Schur decomposition of qudits

plethysm

Using plethysm to compute the Schur decomposition of qudits

This project will compute the Schur functor decomposition of the representation space $V^{\otimes n}$ of $U(d)$ for $n$-qudits of dimension $d$, the canonical example being that of qubits $(\mathbb{C}^2)^{\otimes n}$ for the action of $\mathbf{U}(2), \mathbf{SU}(2), \mathbf{SL}(2)$ or the corresponding Lie algebras $\mathfrak{U}_2$ and $\mathfrak{sl}(2)$ (or $\mathfrak{su}(2)$). See for example $\S 13.3$ of Fulton and Harris and the macaulay2 package described in Schur Complexes