A-Type Open SL(2, ℂ) Spin Chain

For the noncompact open SL(2, ℂ) spin chain, the eigenfunctions of the special matrix element of the 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 calcul...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2025
Hauptverfasser: Antonenko, Pavel V., Derkachov, Sergey É., Valinevich, Pavel A.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2025
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/214186
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:A-Type Open SL(2, ℂ) Spin Chain. Pavel V. Antonenko, Sergey É. Derkachov and Pavel A. Valinevich. SIGMA 21 (2025), 107, 48 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung:For the noncompact open SL(2, ℂ) spin chain, the eigenfunctions of the special matrix element of the 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 the -operator and demonstrate its hidden role. The symmetry of eigenfunctions with respect to the reflection of the spin variable → 1 − is established. The Mellin-Barnes representation for eigenfunctions is derived, and equivalence with the initial coordinate representation is proved. The transformation from one representation to another is grounded on the application of the -type Gustafson integral generalized to the complex field.
ISSN:1815-0659