scholarly journals Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $\boldsymbol{A^{(1)}_{n-1}}$

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Atsuo Kuniba ◽  
Masato Okado
Keyword(s):  
Type A ◽  
Baxter Equation ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Reflection Equation ◽  
Theoretical Reflection

Abstract A trick to obtain a solution to the set-theoretical reflection equation from a known one to the Yang–Baxter equation is applied to crystals and geometric crystals associated to the quantum affine algebra of type $A^{(1)}_{n-1}$.

BRST COHOMOLOGY IN QUANTUM AFFINE ALGEBRA $U_q \left( {\widehat{sl_2 }} \right)$

1994 ◽  
Vol 09 (14) ◽  
pp. 1253-1265 ◽  
Author(s):  
HITOSHI KONNO
Keyword(s):  
Free Field ◽  
Classical Case ◽  
Explicit Construction ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Field Representation ◽  
Highest Weight ◽  
Brst Charge ◽  
Brst Cohomology ◽  
Highest Weight Representation

Using free field representation of quantum affine algebra [Formula: see text], we investigate the structure of the Fock modules over [Formula: see text]. The analysis is based on a q-analog of the BRST formalism given by Bernard and Felder in the affine Kac-Moody algebra [Formula: see text]. We give an explicit construction of the singular vectors using the BRST charge. By the same cohomology analysis as the classical case (q=1), we obtain the irreducible highest weight representation space as a non-trivial cohomology group. This enables us to calculate a trace of the q-vertex operators over this space.

Raising/Lowering Maps and Modules for the Quantum Affine Algebra

2007 ◽  
Vol 35 (7) ◽  
pp. 2140-2159 ◽  
Author(s):  
Darren Funk-Neubauer
Keyword(s):  
Quantum Affine Algebra ◽  
Affine Algebra

scholarly journals The twisted quantum affine algebra Uq(A2(2)) and correlation functions of the Izergin-Korepin model

1999 ◽  
Vol 556 (3) ◽  
pp. 485-504 ◽  
Author(s):  
Bo-Yu Hou ◽  
Wen-Li Yang ◽  
Yao-Zhong Zhang
Keyword(s):  
Correlation Functions ◽  
Quantum Affine Algebra ◽  
Affine Algebra

Two-Dimensional R-Matrices — Descendants of Three-Dimensional R-Matrices

1997 ◽  
Vol 12 (19) ◽  
pp. 1393-1410 ◽  
Author(s):  
S. M. Sergeev
Keyword(s):  
Three Dimensional ◽  
Baxter Equation ◽  
Two Dimensional ◽  
Affine Algebra ◽  
Tetrahedron Equation ◽  
Drinfeld Double ◽  
R Matrix ◽  
Operator Solution ◽  
Dimensional Models ◽  
Three Dimensional Models

Finite layers of three-dimensional models can be regarded as two-dimensional with complicated multi-stated weights. The tetrahedron equation in 3D provides the Yang–Baxter equation for this composite weights in 2D. Such solutions of the Yang–Baxter equation are constructed for the simplest operator solution of the tetrahedron equation. These R-matrices can be regarded as a special projection of universal R-matrix for some Drinfeld double [Formula: see text], associated with the affine algebra [Formula: see text]. Usual R-matrix for [Formula: see text] is another projection of [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document