Imposing rank-one and rank-two shift conditions on symmetric and skew-symmetric moment matrices yields the C-Toda and B-Toda hierarchies with explicit Lax matrices, and shows the Pfaff lattice is the large BKP hierarchy.
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Rank shift conditions and reductions of 2d-Toda theory
Imposing rank-one and rank-two shift conditions on symmetric and skew-symmetric moment matrices yields the C-Toda and B-Toda hierarchies with explicit Lax matrices, and shows the Pfaff lattice is the large BKP hierarchy.