$\mathcal{N}$-extended supersymmetric Calogero models

We propose a new $\mathcal{N}$-extended supersymmetric $su(n)$ spin-Calogero model. Employing a generalized Hamiltonian reduction adopted to the supersymmetric case, we explicitly construct a novel rational $n$-particle Calogero model with an arbitrary even number of supersymmetries. It features $\mathcal{N}{n}^2$ rather than $\mathcal{N}n$ fermionic coordinates and increasingly high fermionic powers in the supercharges and the Hamiltonian.