Completeness of SoV Representation for SL(2, ℝ) Spin Chains

Abstract

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 SL(2, ℝ) spin chains.