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We construct a homomorphism from the affine Yangian$Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n))$ to the affine Yangian$Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n+1))$. We also give therelationship between this homomorphism and the one from the affine Yangian$Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n))$ to the universal envelopingalgebra of the rectangular algebra $\mathcal{W}^k(\mathfrak{gl}(2n),(2^n))$constructed by the author.

A homomorphism from the affine Yangian  $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n))$ to the affine Yangian  associated with $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n+1))$