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\documentclass[12pt,a4paper]{article} \pagestyle{empty} %\textwidth15cm %\textheight22cm \begin{document} \begin{center} Referee's report \end{center} \begin{quote} on the paper ``Inductive limit of representations of Cartan motion groups'' by Lucien Kouassi Yao and Kinvi~Kangni. \end{quote} In the paper, the authors give a construction of irreducible representations of infinite-dimensional Cartan motion group by using the inductive limit techniques. To construct such representations, the authors show that there is a series of embedding of irreducible representation of pre-limit subgroups. The main result states that the limit representation is an irreducible representation of the inductive limit of the Cartan motion groups, and that any irreducible representation of the inductive limit can be obtained as such inductive limit. However, the paper has several serious drawbacks. 1. It is not clear if the author consider unitary representations of purely algebraic ones. Most likely, the representations are assumed unitary (or at least in a Banach space), since they speak on completion etc. 2. In the definition of representations $\Pi_{\mu_n,\lambda_n}$, the Hilbert structure (or norm) should be described. Also, there should be some statement or reference concerning their irreducibility (induced representation can be reducible). 3. The main statement of the paper is Theorem 2.2. which gives a construction of a class of irreducible representations of the inductive limit group. Such a construction is a simple exercise providing the reader is familiar with common techniques of inductive limit representations. 4. ``The converse is also true''. It is not quite clear, if the author assert that any irreducible representation of the inductive limit group can be obtained as a limit of irreducible representations, or this is true for some class of representations only. Generally, the structure of reprsentations of an inductive limit group is very complicated, and it looks suspicious that they all can be obtained in the way described in the paper. 5. The proof of the main theorem is not complete. In fact, it is not proved that $P_n$ is a projection, and it is quite not clear that the restriction of $\Pi_{\mu,\lambda}$ to $G_0(n)$ is irreducible in $V(n)$ and coincides with some $\Pi_{\mu_n,\lambda_n}$. 6. The list of references contains 20 items, but none of them is mentioned in the text of the paper. In our opinion, the paper should be rejected. \bigskip Referees, \bigskip Prof. Yu.S.Samoilenko, Prof. V.L.Ostrovskyi Ins. Math. Nat. Acad. Sci. of Ukraine \end{document}