I will review the QQ-system and oscillator construction of Q-operators for su(r+1) spin chains and discuss its generalisation to so(2r) spin chains. ----- Part of London Integrability Journal Club. If you are a new participant, please register filling the form at integrability-london.weebly.com. The link will be emailed.

I plan to discuss how Q-operators for rational spin chains can be constructed in the framework of the quantum inverse scattering method. The presentation will include open and closed XXX type spin chains with compact and non-compact representations of sl(2) in the quantum space. Further I plan to elaborate on the generalisation to spin chains of higher rank and in particular u(2,2|4) which underlies N=4 super Yang-Mills theory at weak coupling. Finally I will discuss the classification of the oscillator type solutions to the Yang-Baxter equation that are relevant to build Q-operators and give an outlook.