Polyhedral realizations of crystal bases for quantum algebras of classical affine types

Abstract

We give the explicit forms of the crystal bases B(∞) for the quantum affine algebras of types \documentclass[12pt]{minimal}\begin{document}$A^{(2)}_{2n-1}$\end{document}A2n−1(2), \documentclass[12pt]{minimal}\begin{document}$A^{(2)}_{2n}$\end{document}A2n(2), \documentclass[12pt]{minimal}\begin{document}$B^{(1)}_{n}$\end{document}Bn(1), \documentclass[12pt]{minimal}\begin{document}$C^{(1)}_{n}$\end{document}Cn(1), \documentclass[12pt]{minimal}\begin{document}$D^{(1)}_{n}$\end{document}Dn(1), and \documentclass[12pt]{minimal}\begin{document}$D^{(2)}_{n+1}$\end{document}Dn+1(2) by using the method of polyhedral realizations of crystal bases.