Separated variables and wave functions for rational g l (N ) spin chains in the companion twist frame
Abstract
We propose a basis for rational g l (N ) spin chains in an arbitrary rectangular representation (S^{A}) that factorises the Bethe vectors into products of Slater determinants in Baxter Qfunctions. This basis is constructed by repeated action of fused transfer matrices on a suitable reference state. We prove that it diagonalises the socalled Boperator; hence, the operatorial roots of the latter are the separated variables. The spectrum of the separated variables is also explicitly computed, and it turns out to be labeled by GelfandTsetlin patterns. Our approach utilises a special choice of the spin chain twist which substantially simplifies derivations.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 March 2019
 DOI:
 10.1063/1.5085387
 arXiv:
 arXiv:1810.10996
 Bibcode:
 2019JMP....60c2701R
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 37 pages