A-Type Open ${\rm SL}(2,\mathbb{C})$ Spin Chain
Abstract
For the noncompact open spin chain, the eigenfunctions of the special matrix element of monodromy matrix are constructed. The key ingredients of the whole construction are local Yang-Baxter -operators, -operator and raising operators obtained by reduction from the -operator. The calculation of various scalar products and the proof of orthogonality are based on the properties of -operator and demonstrate its hidden role. The symmetry of eigenfunctions with respect to reflection of the spin variable is established. The Mellin-Barnes representation for eigenfunctions is derived and equivalence with initial coordinate representation is proved. The transformation from one representation to another is grounded on the application of -type Gustafson integral generalized to the complex field.
Keywords
Cite
@article{arxiv.2507.09568,
title = {A-Type Open ${\rm SL}(2,\mathbb{C})$ Spin Chain},
author = {Pavel V. Antonenko and Sergey É. Derkachov and Pavel A. Valinevich},
journal= {arXiv preprint arXiv:2507.09568},
year = {2025}
}