Reply to "Comment on 'Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos'"

In the preprint arXiv:2110.08210, some comments on our paper recently published in JHEP \textbf{09} (2021) 053 have been made. Since some of the comments are completely wrong and others are quite misleading, we decide to clarify the relevant issues in a formal reply. First of all, nothing is wrong about our calculations and physical results in the original paper. Second, there is no logical gap to fill at all. The fact that the $N$-dimensional unitary group over the field of complex numbers ${\rm U}(N,\mathbb{C})$ is not a linear algebraic group is actually irrelevant for the validity of the Molien-Weyl formula. As we shall explain in this reply, all the comments in arXiv:2110.08210 arise from the misunderstanding and misinterpretation of our discussions and results.