Yangians and classical Lie algebras

Quantum Group Symmetry in sine-Gordon and Affine Toda Field Theories on the Half-Line

“…We shall denote these algebras Y (g, g σ ) and refer to them as twisted Yangians. Twisted Yangians for g = su(n) have already been described in [27] for g σ = so(n) and g σ = sp(n) and in [26] for g σ = su(m) ⊕ su(n − m) ⊕ u(1).…”

Yangians and their applications

“…By the general approach of Drinfeld [38], the Yangian for sl n should be defined as a quotient algebra of Y(n). The fact that it can also be realized as a (Hopf) subalgebra of Y(n) was observed by Olshanski [119]. 2.9.…”

“…Another proof was given by Levendorskiȋ [97]. The details of the proof outlined here can be found in [119]. It follows the approach of Olshanskiȋ [138].…”

“…The basic ideas and formulas associated with the quantum determinant for an arbitrary n are contained in Kulish-Sklyanin's survey paper [89]. Detailed proofs are given in [119]. Proposition 2.14 is contained e.g.…”

Analytical Bethe ansatz in gl(N) spin chains

“…The underlying algebraic structure is now the twisted Yangian [9,10], whose exchange relations are (ρ = − N 2 ):…”