Felder's Elliptic Quantum Group and Elliptic Hypergeometric Series on the Root System An

2010 ◽  
Author(s):  
H. Rosengren
Keyword(s):  
Quantum Group ◽  
Root System ◽  
Hypergeometric Series ◽  
Elliptic Quantum

scholarly journals WAKIMOTO REALIZATION OF THE ELLIPTIC QUANTUM GROUP $U_{q,p}(\widehat{{\rm sl}_N})$

2009 ◽  
Vol 24 (30) ◽  
pp. 5561-5578
Author(s):  
TAKEO KOJIMA
Keyword(s):  
Quantum Group ◽  
Free Field ◽  
Quantum Algebra ◽  
Free Field Realization ◽  
Wakimoto Realization ◽  
Arbitrary Level ◽  
Elliptic Quantum

We construct a free field realization of the elliptic quantum algebra [Formula: see text] for arbitrary level k ≠ 0, -N. We study Drinfeld current and the screening current associated with [Formula: see text] for arbitrary level k. In the limit p → 0 this realization becomes q-Wakimoto realization for [Formula: see text].

scholarly journals Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sl2)

1996 ◽  
Vol 480 (1-2) ◽  
pp. 485-503 ◽  
Author(s):  
Giovanni Felder ◽  
Alexander Varchenko
Keyword(s):  
Quantum Group ◽  
Bethe Ansatz ◽  
Algebraic Bethe Ansatz ◽  
Elliptic Quantum

scholarly journals The dynamical Yang–Baxter relation and the minimal representation of the elliptic quantum group

2003 ◽  
Vol 44 (3) ◽  
pp. 1276-1296
Author(s):  
Heng Fan ◽  
Boyu Hou ◽  
Kangjie Shi ◽  
Ruihong Yue ◽  
Shaoyou Zhao
Keyword(s):  
Quantum Group ◽  
Minimal Representation ◽  
Elliptic Quantum

Small Elliptic Quantum Group

2001 ◽  
Vol 1 (2) ◽  
pp. 243-286 ◽  
Author(s):  
V. Tarasov ◽  
A. Varchenko
Keyword(s):  
Quantum Group ◽  
Elliptic Quantum

Representation of the boundary elliptic quantum group BEτ,η(sl2) and the Bethe ansatz

1997 ◽  
Vol 496 (3) ◽  
pp. 551-570 ◽  
Author(s):  
Heng Fan ◽  
Bo-Yu Hou ◽  
Kang-he Shi
Keyword(s):  
Quantum Group ◽  
Bethe Ansatz ◽  
Elliptic Quantum

FUSION CONSTRUCTION OF THE VERTEX OPERATORS IN HIGHER LEVEL REPRESENTATION OF THE ELLIPTIC QUANTUM GROUP

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1995-2001
Author(s):  
HITOSHI KONNO
Keyword(s):  
Quantum Group ◽  
Free Field ◽  
Vertex Operators ◽  
Type I ◽  
Field Representation ◽  
Short Summary ◽  
Higher Spin ◽  
Elliptic Algebra ◽  
Elliptic Quantum ◽  
Weight Coefficients

After a short summary on the elliptic quantum group [Formula: see text] and the elliptic algebra [Formula: see text], we present a free field representation of the Drinfeld currents and the vertex operators (VO's) in the level k. We especially demonstrate a construction of the higher spin type I VO's by fusing the spin 1/2 type I VO's and fix a rule of attaching the screening current S(z) associated with the q-deformed ℤk-parafermion theory. As a result we get a free field representation of the higher spin type I VO's which commutation relation by the fused Boltzmann weight coefficients is manifest.

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