Classification of solutions to Toda systems of types C and B with singular sources

In this paper, the classification in Lin et al. (Invent. Math. 190(1):169–207, 2012) of solutions to Toda systems of type A with singular sources is generalized to Toda systems of types C and B. Like in the A case, the solution space is shown to be parametrized by the abelian subgroup and a subgroup of the nilpotent subgroup in the Iwasawa decomposition of the corresponding complex simple Lie group. The method is by studying the Toda systems of types C and B as reductions of Toda systems of type A with symmetries. The theories of Toda systems as integrable systems as developed in Leznov (Teoret. Mat. Fiz. 42(3):343–349, 1980), Leznov and Saveliev (Group-theoretical methods for integration of nonlinear dynamical systems, Progress in Physics, vol. 15. Birkhauser, Verlag, 1992), Nie (J. Geom. Phys. 62(12):2424–2442, 2012), Nie (J. Nonlinear Math. Phys. 21(1):120–131, 2014), in particular the W-symmetries and the iterated integral solutions, play essential roles in this work, together with certain characterizing properties of minors of symplectic and orthogonal matrices.