New Combinatorial Formulae for Nested Bethe Vectors

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Authors: Kosmakov, Maksim, Tarasov, Vitaly
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/213516
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: New Combinatorial Formulae for Nested Bethe Vectors. Maksim Kosmakov and Vitaly Tarasov. SIGMA 21 (2025), 060, 28 pages

We give new combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for the evaluation modules over the Yangian Y(₄). The case of Y(ₙ) for an arbitrary n is considered in [Lett. Math. Phys. 115 (2025), 12, 20 pages, arXiv:2402.15717].