Abstract
We study integrable cutoff constraints for a semidiscrete Toda lattice. We construct a Lax representation for a semidiscrete analogue of lattices corresponding to simple Lie algebras of the C series. We introduce nonlocal variables in terms of which the symmetries of the infinite semidiscrete lattice can be expressed, and we classify cutoff constraints of a certain form compatible with the symmetries of the infinite lattice.
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