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

References in corpus (2)

• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Essays on the theory of elliptic hypergeometric functions

Cited by in corpus (3)

• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Unitarity of the SoV Transform for $\mathrm{SL}(2,\mathbb{C})$ Spin Chains
• The Gelfand-Tsetlin basis for infinite-dimensional representations of $g{l}_n(\mathbb{C})$