The authors show how to interpret recent results of Moser and Veselov on discrete
versions of a class of classical integrable systems, in terms of a loop group framework. In
this framework the discrete systems appear as time-one maps of integrable Hamiltonian
flows. Earlier results of Moser on isospectral deformations of rank 2 extensions of a fixed
matrix, can also be incorporated into their scheme.
Key words: Hamiltonian mechanics, integrable systems, loop groups, 7?-matrices, discrete
Euler-Arnold equation, billiard map, rank 2 extensions.