  We review arXiv:1308.3444 and arXiv:1104.1891. The structure of the spectrum
of a quantum integrable system is crucial to understand its properties. In his
seminar 1971 paper, Baxter observed that the spectrum of the "ice model" has a
very remarkable form involving polynomials. Then it was conjectured that analog
polynomials can be used to describe the spectra of more general quantum
integrable systems (arXiv:math/9810055). We discuss how these (generalized
Baxter's) polynomials arise naturally in terms of representation theory. This
result lead recently to the proof of the conjecture.
