A-Type Open \rm SL(2,ℂ) Spin Chain

2025/07/13 by P. V. Antonenko, Antonenko, Pavel V., S. Derkachov +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2507.09568

openalex publication_date 2025/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

For the noncompact open \rm SL(2,ℂ) 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 R-operators, Q-operator and raising operators obtained by reduction from the Q-operator. The calculation of various scalar products and the proof of orthogonality are based on the properties of Q-operator and demonstrate its hidden role. The symmetry of eigenfunctions with respect to reflection of the spin variable s → 1-s 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 A-type Gustafson integral generalized to the complex field.

Citations

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