Bi-linear finite difference Hirota equation and the related Y-system appear to be a key tool of study of many quantum integrable systems. Focussing on the examples of supersymmetric spin chains and of the SU(N) Principal Chiral Field sigma-model at finite volume, we show how the Hirota relation emerges, and how it can be solved in terms of Baxter’s Q-operators. Recent construction of these operators in terms of co-derivatives will be introduced in the case of (super)spin-chains, and the applications of Q-functions to some sigma models will be sketched out.

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