Tarasov, VitalyKosmakov, MaksimIts, AlexanderMukhin, EvgenyRamras, Daniel2023-08-312023-08-312022-08https://hdl.handle.net/1805/35264Indiana University-Purdue University Indianapolis (IUPUI)We 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.en-USIntegrable modelsRiemann-Hilbert problemNested Algebraic Bethe ansatztt* equationYangiansThesis