A generalizedQ-operator forU_qvertex models

Factorization of the transfer matrices for the quantumsell(2) spin chains and Baxter equation

“…The same equation holds for the Q operator as well. The first relation (n = −m = 1/2) among the ones in (4.11) is nothing else but the Baxter equation 12) where…”

“…The Baxter Q−operator is known for a large number of integrable models [6,7,8,9,10,11,12,13,14,15]. Nevertheless, a universal method for obtaining of the Baxter operator is absent so far and each model (or class of models) needs a special consideration.…”

Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz

“…Rossi and Weston introduced in [19] the following infinite-dimensional four-parameter representation π + = π + (w; s 0 , s 1 , s 2 ) of the upper Borel subalgebra U q (b + ),…”

“…[15]. These new methods are based on the representation theory of quantum groups [16,17,18,19,1]. The latter method will be of importance to us as the auxiliary matrices constructed in this manner, see [1,2], have been shown for several examples to yield information on the irreducible representations of the symmetry algebra at roots of unity.…”

Baxter operators for the noncompact quantumsl(3) invariant spin chain

“…The Baxter operators for these models and some others were constructed in Refs. [8,9,10,11,12,13,14,15,16,17,18,19,20,21]. For example, Baxter operators for a different kind of the sl(2) magnets can be obtained with the help of the Pasquier-Gaudin trick [8].…”