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Item Certain Aspects of Quantum and Classical Integrable Systems(2022-08) Kosmakov, Maksim; Tarasov, Vitaly; Its, Alexander; Mukhin, Evgeny; Ramras, DanielWe derive new combinatorail formulas for vector-valued weight functions for the evolution modules over the Yangians Y (gl_n). We obtain them using the Nested Algebraic Bethe ansatz method. We also describe the asymptotic behavior of the radial solutions of the negative tt* equation via the Riemann-Hilbert problem and the Deift-Zhou nonlinear steepest descent method.