An integrable vertex model and the quantum affine algebra at the critical level

2002 ◽  
Vol 638 (3) ◽  
pp. 291-327 ◽  
Author(s):  
R.M. Gade
Keyword(s):  
Critical Level ◽  
Vertex Model ◽  
Quantum Affine Algebra ◽  
Affine Algebra

scholarly journals QUANTUM AFFINE SYMMETRY IN VERTEX MODELS

1993 ◽  
Vol 08 (08) ◽  
pp. 1479-1511 ◽  
Author(s):  
MAKOTO IDZUMI ◽  
TETSUJI TOKIHIRO ◽  
KENJI IOHARA ◽  
MICHIO JIMBO ◽  
TETSUJI MIWA ◽  
...  
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Spin Chain ◽  
Vertex Model ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Affine Symmetry ◽  
Higher Spin ◽  
Local Operators ◽  
The One

We study the higher spin analogs of the six-vertex model on the basis of its symmetry under the quantum affine algebra [Formula: see text]. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer matrix, vacuum, creation/ annihilation operators of particles, and local operators, purely in the language of representation theory. We find that, regardless of the level of the representation involved, the particles have spin 1/2, and that the n-particle space has an RSOS type structure rather than a simple tensor product of the one-particle space. This agrees with the picture proposed earlier by Reshetikhin.

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.

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 $A^{(1)}_{n-1}$.

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