scholarly journals The quantum determinant of the elliptic algebra $ {\mathcal{A}_{q, p}(\mathfrak{\widehat{gl}}_N)}$

2018 ◽  
Vol 51 (44) ◽  
pp. 445201 ◽  
Author(s):  
L Frappat ◽  
D Issing ◽  
E Ragoucy
Keyword(s):  
Elliptic Algebra ◽  
Quantum Determinant

scholarly journals The elliptic algebra and the deformation ofWNalgebra

2003 ◽  
Vol 37 (2) ◽  
pp. 371-383 ◽  
Author(s):  
Takeo Kojima ◽  
Hitoshi Konno
Keyword(s):  
Elliptic Algebra

scholarly journals Elliptic Algebra $\Uqp(\slthbig)$ : Drinfeld Currents and Vertex Operators

1999 ◽  
Vol 199 (3) ◽  
pp. 605-647 ◽  
Author(s):  
Michio Jimbo ◽  
Hitoshi Konno ◽  
Satoru Odake ◽  
Jun'ichi Shiraishi
Keyword(s):  
Vertex Operators ◽  
Elliptic Algebra

scholarly journals The superconformal index and an elliptic algebra of surface defects

2014 ◽  
Vol 2014 (10) ◽  
Author(s):  
Mathew Bullimore ◽  
Martin Fluder ◽  
Lotte Hollands ◽  
Paul Richmond
Keyword(s):  
Surface Defects ◽  
Superconformal Index ◽  
Elliptic Algebra

scholarly journals ELLIPTIC ALGEBRA AND INTEGRABLE MODELS FOR SOLITONS ON NONCOMMUTATIVE TORUS $\mathcal T$

2002 ◽  
Vol 16 (14n15) ◽  
pp. 2079-2087 ◽  
Author(s):  
BO-YU HOU ◽  
DAN-TAO PENG
Keyword(s):  
Hilbert Space ◽  
Heisenberg Group ◽  
Integrable Models ◽  
Transfer Matrices ◽  
Noncommutative Torus ◽  
Quantum Operator ◽  
Elliptic Algebra

We study the algebra [Formula: see text], the basis of the Hilbert space ℋn in terms of θ functions of the positions of n solitons. Then we embed the Heisenberg group as the quantum operator factors in the representation of the transfer matrices of various integrable models. Finally we generalize our result to the generic θ case.

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.

scholarly journals The dynamicalU(n)quantum group

2006 ◽  
Vol 2006 ◽  
pp. 1-30 ◽  
Author(s):  
Erik Koelink ◽  
Yvette Van Norden
Keyword(s):  
Quantum Group ◽  
Matrix Algebra ◽  
Exterior Algebra ◽  
Matrix Elements ◽  
Algebra Representation ◽  
The Matrix ◽  
Quantum Minor ◽  
Quantum Determinant

We study the dynamical analogue of the matrix algebraM(n), constructed from a dynamicalR-matrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these corepresentations. These elements are studied in more detail, especially the action of the comultiplication and Laplace expansions. Using the Laplace expansions we can prove that the dynamical quantum determinant is almost central, and adjoining an inverse the antipode can be defined. This results in the dynamicalGL(n)quantum group associated to the dynamicalR-matrix. We study a∗-structure leading to the dynamicalU(n)quantum group, and we obtain results for the canonical pairing arising from theR-matrix.

scholarly journals FREE FIELD CONSTRUCTIONS FOR THE ELLIPTIC ALGEBRA $\rscr{A}_{q,p}(\widehat{sl}_2)$ AND BAXTER'S EIGHT-VERTEX MODEL

2004 ◽  
Vol 19 (supp02) ◽  
pp. 363-380 ◽  
Author(s):  
J. SHIRAISHI
Keyword(s):  
Integral Formula ◽  
Free Field ◽  
Virasoro Algebra ◽  
Vertex Operators ◽  
Vertex Model ◽  
Elliptic Algebra ◽  
Deformed Virasoro Algebra ◽  
The One ◽  
Level 2 ◽  
Elliptic Quantum

Three examples of free field constructions for the vertex operators of the elliptic quantum group [Formula: see text] are obtained. Two of these ( for p1/2=±q3/2, p1/2=-q2) are based on representation theories of the deformed Virasoro algebra, which correspond to the level 4 and level 2 Z-algebra of Lepowsky and Wilson. The third one (p1/2=q3) is constructed over a tensor product of a bosonic and a fermionic Fock spaces. The algebraic structure at (p1/2=q3), however, is not related to the deformed Virasoro algebra. Using these free field constructions, an integral formula for the correlation functions of Baxter's eight-vertex model is obtained. This formula shows different structure compared with the one obtained by Lashkevich and Pugai.

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