Generalized Loop Modules for Affine Kac–Moody Algebras

2014 ◽  
pp. 175-183
Author(s):  
Vyacheslav Futorny ◽  
Iryna Kashuba
Keyword(s):  
Loop Modules

Quantum loop modules

2003 ◽  
Vol 7 (3) ◽  
pp. 56-80 ◽  
Author(s):  
Vyjayanthi Chari ◽  
Jacob Greenstein
Keyword(s):  
Loop Modules

scholarly journals QUANTUM LOOP MODULES AND QUANTUM SPIN CHAINS

1994 ◽  
Vol 09 (22) ◽  
pp. 3925-3958
Author(s):  
DANIEL ALTSCHULER ◽  
BRIAN DAVIES
Keyword(s):  
Sufficient Conditions ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Affine Algebra ◽  
Quantum Spin Chains ◽  
Affine Algebra ◽  
Highest Weight ◽  
Necessary And Sufficient ◽  
Loop Modules

We construct level-0 modules of the quantum affine algebra [Formula: see text], as the q-deformed version of the Lie algebra loop module construction. We give necessary and sufficient conditions for the modules to be irreducible. We construct the crystal base for some of these modules and find significant differences from the case of highest weight modules. We also consider the role of loop modules in the recent scheme for diagonalizing certain quantum spin chains using their [Formula: see text] symmetry.

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