\begin{thebibliography}{99}
\raggedright
\bibitem{BR} A. Berenstein and D. Rupel, \emph{Quantum cluster characters of Hall algebras}, \href{https://arxiv.org/abs/1308.2992v2}{arXiv:1308.2992v2} (2014).
\bibitem{BZ} A. Berenstein and A. Zelevinsky, \emph{Quantum cluster algebras}, \href{https://arxiv.org/abs/math/0404446v2}{arXiv:math/0404446v2} (2004).
\bibitem{Davison} B. Davison, \emph{Positivity for quantum cluster algebras}, \href{https://arxiv.org/abs/1601.07918v6}{arXiv:1601.07918v6} (2017).
\bibitem{K1} M. Kashiwara, M. Kim, S.-j. Oh and E. Park, \emph{Localizations for quiver Hecke algebras}, \href{https://arxiv.org/abs/1901.09319v2}{arXiv:1901.09319v2} (2020).
\bibitem{K2} M. Kashiwara, M. Kim, S.-j. Oh and E. Park, \emph{Localizations for quiver Hecke algebras II}, \href{https://arxiv.org/abs/2208.01255v1}{arXiv:2208.01255v1} (2022).
\bibitem{K3} M. Kashiwara, M. Kim, S.-j. Oh and E. Park, \emph{Laurent family of simple modules over quiver Hecke algebra}, \href{https://arxiv.org/abs/2306.15181v1}{arXiv:2306.15181v1} (2023).
\bibitem{Kleshchev} A. Kleshchev, \emph{Lectures on Infinite Dimensional Lie Algebras}, lecture notes, University of Oregon, undated. \href{https://pages.uoregon.edu/klesh/teaching/IDLALN.pdf}{Author's online notes} (accessed 27 September 2026).
\bibitem{LV} A. D. Lauda and M. Vazirani, \emph{Crystals from categorified quantum groups}, \href{https://arxiv.org/abs/0909.1810v2}{arXiv:0909.1810v2} (2011).
\bibitem{LS} K. Lee and R. Schiffler, \emph{Positivity for cluster algebras}, Ann. of Math. \textbf{182} (2015), 73--125. \href{https://arxiv.org/abs/1306.2415v3}{arXiv:1306.2415v3}.
\bibitem{Murata} H. Murata, \emph{A diagrammatic approach to reflection functors}, \href{https://arxiv.org/abs/2506.17070v4}{arXiv:2506.17070v4}, 28 August 2026.
\bibitem{RupelCC} D. Rupel, \emph{Quantum cluster characters}, \href{https://arxiv.org/abs/1109.6694v2}{arXiv:1109.6694v2} (2012).
\bibitem{Feigin} D. Rupel, \emph{The Feigin tetrahedron}, SIGMA \textbf{11} (2015), 024, 30 pp. \href{https://arxiv.org/abs/1401.4338v2}{arXiv:1401.4338v2}. \href{https://doi.org/10.3842/SIGMA.2015.024}{doi:10.3842/SIGMA.2015.024}.
\bibitem{Speyer} D. E. Speyer, \emph{Powers of Coxeter elements in infinite groups are reduced}, \href{https://arxiv.org/abs/0710.3188v1}{arXiv:0710.3188v1} (2007).
\bibitem{TW} P. Tingley and B. Webster, \emph{Mirkovi\'c--Vilonen polytopes and Khovanov--Lauda--Rouquier algebras}, \href{https://arxiv.org/abs/1210.6921v5}{arXiv:1210.6921v5} (2015).
\bibitem{Tran} T. Tran, \emph{F-polynomials in quantum cluster algebras}, \href{https://arxiv.org/abs/0904.3291v1}{arXiv:0904.3291v1} (2009).
\end{thebibliography}