scholarly journals Quasi-Hopf superalgebras and elliptic quantum supergroups

1999 ◽  
Vol 40 (10) ◽  
pp. 5264-5282 ◽  
Author(s):  
Yao-Zhong Zhang ◽  
Mark D. Gould
Keyword(s):  
Elliptic Quantum

scholarly journals Elliptic quantum groups and Baxter relations

2018 ◽  
Vol 12 (3) ◽  
pp. 599-647 ◽  
Author(s):  
Huafeng Zhang
Keyword(s):  
Quantum Groups ◽  
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 8V CSOS MODEL AND THE sl2 LOOP ALGEBRA SYMMETRY OF THE SIX-VERTEX MODEL AT ROOTS OF UNITY

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1899-1905 ◽  
Author(s):  
TETSUO DEGUCHI
Keyword(s):  
Transfer Matrix ◽  
Lattice Model ◽  
Algebraic Method ◽  
System Size ◽  
Spin Operator ◽  
Total Spin ◽  
Coupling Constants ◽  
Roots Of Unity ◽  
Vertex Model ◽  
Elliptic Quantum

We review an algebraic method for constructing degenerate eigenvectors of the transfer matrix of the eight-vertex Cyclic Solid-on-Solid lattice model (8V CSOS model), where the degeneracy increases exponentially with respect to the system size. We consider the elliptic quantum group Eτ,η(sl2) at the discrete coupling constants: 2N η = m1 + im2τ, where N, m1 and m2 are integers. Then we show that degenerate eigenvectors of the transfer matrix of the six-vertex model at roots of unity in the sector SZ ≡ 0 ( mod N) are derived from those of the 8V CSOS model, through the trigonometric limit. They are associated with the complete N strings. From the result we see that the dimension of a given degenerate eigenspace in the sector SZ ≡ 0 ( mod N) of the six-vertex model at Nth roots of unity is given by [Formula: see text], where [Formula: see text] is the maximal value of the total spin operator SZ in the degenerate eigenspace.

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