Primitive ideals of $\mathrm{U}(\mathfrak{s}\mathfrak{l}(\mathrm{\infty }))$

We provide an explicit description of the primitive ideals of the enveloping algebra $\mathrm{U}(\mathfrak{s}\mathfrak{l}(\mathrm{\infty }))$ of the infinite-dimensional finitary Lie algebra $\mathfrak{s}\mathfrak{l}(\mathrm{\infty })$ over an uncountable algebraically closed field of characteristic 0. Our main new result is that any primitive ideal of $\mathrm{U}(\mathfrak{s}\mathfrak{l}(\mathrm{\infty }))$ is integrable. A classification of integrable primitive ideals of $\mathrm{U}(\mathfrak{s}\mathfrak{l}(\mathrm{\infty }))$ has been known previously, and relies on the pioneering work of A. Zhilinskii.