By taking the concept of weight conservation into account, new solutions of Yang-Baxter equation without spectral parameter are obtained through the non-standard R-matrix on the tensorial space V 1/2 ⊗ V j ( j ≠ 1/2) in terms of the irreducible representation of the quantum universal enveloping algebra SL q (2). The non-standard R-matrix R 1/2 1 is obtained in an explicit form for j = 1.

Chinese Physics LettersOct 1, 19910 citations

R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain

Sergey E. Derkachov

The problem of constructing the SL(N, C) invariant solutions to the Yang-Baxter equation is considered.The solutions (R-operators) for arbitrarily principal series representations of SL(N, C) are obtained in an explicit form.We construct the commutative family of the operators Q k (u) which can be identified with the Baxter operators for the noncompact SL(N, C) spin magnet.

arXiv:nlin/0612003Symmetry Integrability and Geometry Methods and ApplicationsDec 2, 200637 citations