Affine q-deformed symmetry and the classical Yang-Baxter σ-model

The Yang-Baxter σ-model is an integrable deformation of the principal chiral model on a Lie group G. The deformation breaks the G×G symmetry to U(1)^rank(G)×G. It is known that there exist non-local conserved charges which, together with the unbroken U(1)^rank(G) local charges, form a Poisson algebra U_q(g), which is the semiclassical limit of the quantum group U_q(g), with g the Lie algebra of G. For a general Lie group G with rank(G)>1, we extend the previous result by constructing local and non-local conserved charges satisfying all the defining relations of the infinite-dimensional Poisson algebra U_q(Lg), the classical analogue of the quantum loop algebra U_q(Lg), where Lg is the loop algebra of g. Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ-model.