We compute by means of the Bethe Ansatz the boundary S matrix for the open anisotropic spin-12 chain with diagonal boundary magnetic fields in the noncritical regime (∆ > 1). Our result, which is formulated in terms of q-gamma functions, agrees with the vertex-operator result of Jimbo et al.

We derive the Faddeev-Reshetikhin (FR) model from a four-dimensional Chern- Simons theory with two order surface defects by following work Costello and Yamazaki [arXiv:1908.02289]. Then we present trigonometric deformation of FR employing boundary condition an R-operator Drinfeld-Jimbo type. This is generalization Delduc, Lacroix, Magro Vicedo [arXiv:1909.13824] disorder defect case to one.

The quantum groupUq(g) associated with a simple Lie algebra g is an associative algebra over the rational function field C(q) (q is an indeterminate) and we can define its ”integral” form over the Laurant polynomial ring C[q, q], which enables us to specialize q to any non-zero complex number ε. We are going to see two types of such integral forms and accordingly, we obtain two types of special...

Aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable Cartan matrices are studied. The irreducible integrable highest weight representations are classified, and shown to be deformations of their classical counterparts. It is also shown that Jimbo type quantum affine superalgebras can be obtained by deforming universal enveloping alge...

Let U be the quantized enveloping algebra associated to a simple Lie algebra g by Drinfel’d and Jimbo. Let λ be a classical fundamental weight for g, and V (λ) the irreducible, finite-dimensional type 1 highest weight U -module with highest weight λ. We show that the canonical basis for V (λ) (see Kashiwara [6, §0] and Lusztig [18, 14.4.12]) and the standard monomial basis (see [11, §§2.4 & 2.5...