Latent symmetries in the six-vertex model of statistical physics

A transfer matrix in the six-vertex model of the two-dimensional physics commutes with many (more compicated) transfer matrices which, in general, do not commute with each other. The study of their action on eigenspaces of a transfer matrix in the six-vertex model is possible due to a “multiplicative property” of the vacuum curves of $\mathcal L$-operators which form the transfer matrices. In particular, this approach enables us to find out the fact that the dimensions of the eigenspaces mentioned above must be multiple to (sufficiently large) powers of number 2. Bibliography: 14 titles.