}   \xymatrix{     K\mathcal{M}(\mathfrak{g},K,I_{X_{G}}) \ar[r]^{\Phi_{X_G}} & K\mathcal{P}(X_G,K)\\     K\mathcal{M}(\mathfrak{l},K_{L},I_{X_{L}}) \ar[u]^{\mathscr{R}_{(\mathfrak{l},K_{L})}^{(\mathfrak{g},K)}}\ar[r]^{\Phi_{X_L}} & K\mathcal{P}(X_