We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang–Baxter equation. Here we generalize our approach from the fundamental representation of to generic finite-dimensional representations in quantum space. The results equally apply to non-compact representations of highest or lowest weight type. We furthermore fill an apparent gap in the literature, and provide the nearest-neighbor Hamiltonians of the spin chains in question for all cases where the representations are described by rectangular Young diagrams, as well as for their infinite-dimensional generalizations. They take the form of digamma functions depending on operator-valued shifted weights.
Baxter Operators and Hamiltonians for 'nearly all' Integrable Closed () Spin Chains / Frassek, R; Lukowski, T; Meneghelli, C; Staudacher, M. - In: NUCLEAR PHYSICS. B. - ISSN 0550-3213. - 874:2(2013), pp. 620-646. [10.1016/j.nuclphysb.2013.06.006]