Completeness of SoV representation for $\mathrm{SL}(2,\mathbb R)$ spin chains

S. E. Derkachov, K. K. Kozlowski, A. N. Manashov

Published 2021-02-26Version 1

This work develops a new method, based on the use of Gustafson's integrals and on the evaluation of singular integrals, allowing one to establish the unitarity of the separation of variables transform for infinite dimensional representations of rank one quantum integrable models. We examine in detail the case of the $\mathrm{SL}(2,\mathbb R)$ spin chains.