scholarly journals $$R$$ R -Matrix Realization of Two-Parameter Quantum Group $$U_{r,s}(\mathfrak {gl}_n)$$ U r , s ( gl n )

2014 ◽  
Vol 2 (3-4) ◽  
pp. 211-230 ◽  
Author(s):  
Naihuan Jing ◽  
Ming Liu
Keyword(s):  
Quantum Group ◽  
R Matrix ◽  
Two Parameter

scholarly journals R matrix for generalized quantum group of type A

2021 ◽  
Vol 566 ◽  
pp. 309-341
Author(s):  
Jae-Hoon Kwon ◽  
Jeongwoo Yu
Keyword(s):  
Quantum Group ◽  
Type A ◽  
R Matrix

scholarly journals A TWO-PARAMETER DEFORMED SUSY ALGEBRA FOR SUp/q(n)-COVARIANT (p,q)-DEFORMED FERMIONIC OSCILLATORS

2005 ◽  
Vol 20 (08) ◽  
pp. 613-622 ◽  
Author(s):  
ABDULLAH ALGIN ◽  
METIN ARIK
Keyword(s):  
Quantum Group ◽  
Fock Space ◽  
Space Representation ◽  
Oscillator Algebra ◽  
Two Parameter

We construct a two-parameter deformed SUSY algebra by constructing SUSY generators which are bilinears of n (p,q)-deformed fermions covariant under the quantum group SU p/q(n) and n undeformed bosons. The Fock space representation of the algebra constructed is discussed and the total deformed Hamiltonian for such a system is obtained. Some physical applications of the quantum group covariant two-parameter deformed fermionic oscillator algebra are also considered.

scholarly journals Multiparametric and Colored Extensions of the Quantum Group GLq(N) and the Yangian Algebra Y(glN) Through a Symmetry Transformation of the Yang–Baxter Equation

1997 ◽  
Vol 12 (05) ◽  
pp. 945-962 ◽  
Author(s):  
B. Basu-Mallick ◽  
P. Ramadevi ◽  
R. Jagannathan
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Spectral Parameter ◽  
General Relation ◽  
Symmetry Transformation ◽  
Baxter Equation ◽  
Color Parameter ◽  
R Matrix ◽  
General Symmetry ◽  
Yangian Algebra

Inspired by Reshetikhin's twisting procedure to obtain multiparametric extensions of a Hopf algebra, a general "symmetry transformation" of the "particle conserving" R-matrix is found such that the resulting multiparametric R-matrix, with a spectral parameter as well as a color parameter, is also a solution of the Yang–Baxter equation (YBE). The corresponding transformation of the quantum YBE reveals a new relation between the associated quantized algebra and its multiparametric deformation. As applications of this general relation to some particular cases, multiparametric and colored extensions of the quantum group GL q(N) and the Yangian algebra Y(glN) are investigated and their explicit realizations are also discussed. Possible interesting physical applications of such extended Yangian algebras are indicated.

scholarly journals REMARKS ON THE QUANTUM GROUP STRUCTURE OF THE RATIONAL c<1 CONFORMAL THEORIES

1991 ◽  
Vol 06 (27) ◽  
pp. 4859-4884 ◽  
Author(s):  
P. FURLAN ◽  
A. CH. GANCHEV ◽  
V.B. PETKOVA
Keyword(s):  
Quantum Group ◽  
Group Structure ◽  
Extended Formulation ◽  
Conformal Blocks ◽  
Fusion Rules ◽  
R Matrix ◽  
Linear Relations ◽  
Intermediate States

The rational c<1 theories are reconsidered beyond the space of BRST states, allowing for intermediate states not contained in the Kac table. The intertwining properties of the screening charges Qm and Qp−m are used to derive linear relations for the general conformal blocks. The fusion rules are recovered on BRST states, combining these relations with previously obtained identities for the fusion matrices, due to the corresponding [Formula: see text]-invariant operators. The extended formulation is applied to give meaning for qp=1 to the quantum group covariant conformal correlations initiated by Moore and Reshetikhin. The correlations are manifestly covariant under the action of the R matrix and in the diagonal case they coincide with the averages of the screened vertices, recently proposed by Gómez and Sierra.

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