Universal K-matrix and Fused K-operators in Quantum Affine Algebras

Explore the concept of universal K-matrices and fused K-operators in a 25-minute conference talk delivered by Guillaume Lemarthe at the Workshop on Integrable systems, exactly solvable models and algebras. Delve into the recent progress made in understanding universal K-matrices for K-operators solving the reflection equation with a spectral parameter. Examine the general framework of universal K-matrices, extending the approach introduced by Appel-Vlaar. Learn about the definition of a universal K-matrix in B⊗H, where H is a Hopf algebra with a universal R-matrix and B is a right H-comodule algebra. Investigate the main example using the quantum affine algebra for sl_2 and the alternating central extension of the q-Onsager algebra. Discover the explicit construction of fused K-operators using intertwining operators and explore the conjecture relating these operators to evaluations of a universal K-matrix. Finally, understand the construction of the transfer matrix and its applications, including the derivation of the TT-relation and specializations to generic open spin-chains.