Related papers: $q$-Deformed Chern Characters for Quantum Groups $…
In this paper, from the $q$-gauge covariant condition we define the $q$-deformed Killing form and the second $q$-deformed Chern class for the quantum group $SU_{q}(2)$. Developing Zumino's method we introduce a $q$-deformed homotopy…
In this paper all deformations of the general linear group, subject to certain restrictions which in particular ensure a smooth passage to the Lie group limit, are obtained. Representations are given in terms of certains sets of creation…
We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge…
All bicovariant first order differential calculi on the quantum group GLq(3,C) are determined. There are two distinct one-parameter families of calculi. In terms of a suitable basis of 1-forms the commutation relations can be expressed with…
We show that application of quantum unitary groups, in place of ordinary flavor SU(n_f), to such static aspects of hadron phenomenology as hadron masses and mass formulas is indeed fruitful. The so-called q-deformed mass formulas are given…
A scheme for treating the pairing of nucleons in terms of generators of Quantum Group SU_{q}(2) is presented. The possible applications to nucleon pairs in a single orbit, multishell case, pairing vibrations and superconducting nuclei are…
The Cartan-Maurer equations for any $q$-group of the $A_{n-1}, B_n, C_n, D_n$ series are given in a convenient form, which allows their direct computation and clarifies their connection with the $q=1$ case. These equations, defining the…
We develop the theory of $q$-characters for quantum affine superalgebras of type $A$ in connection with deformed Cartan matrices. To achieve this, we establish a Khoroshkin-Tolstoy-type multiplicative formula of the universal $R$-matrix of…
Improving on an earlier proposal, we construct the gauge theories of the quantum groups $U_q(N)$. We find that these theories are consistent also with an ordinary (commuting) spacetime. The bicovariance conditions of the quantum…
We study junctions of Wilson lines in refined SU(N) Chern-Simons theory and their local relations. We focus on junctions of Wilson lines in antisymmetric and symmetric powers of the fundamental representation and propose a set of local…
The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
This paper develops a framework for the Hamiltonian quantization of complex Chern-Simons theory with gauge group $\mathrm{SL}(2,\mathbb{C})$ at an even level $k\in\mathbb{Z}_+$. Our approach follows the procedure of combinatorial…
We construct a Chern-Simons action for q-deformed gauge theory which is a simple and straightforward generalization of the usual one. Space-time continues to be an ordinary (commuting) manifold, while the gauge potentials and the field…
Three-dimensional bicovariant differential calculus on the quantum group SU_q(2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U(1). Explicit representations of possible q-deformed…
Based on results for real deformation parameter q we introduce a compact non- commutative structure covariant under the quantum group SOq(3) for q being a root of unity. To match the algebra of the q-deformed operators with necesarry…
We construct quantum deformation of Poincar\'e group using as a starting point $SU(2,2)$ conformal group and twistor-like definition of the Minkowski space. We obtain quantum deformation of $SU(2,2)$ as a real form of multiparametric…
A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show these new ladder operators satisfy new q-deformed commutation relations. In this context we…
Quantum superalgebras $su_{q}(m\mid n)$ are studied in the framework of $R$-matrix formalism. Explicit parametrization of $L^{(+)}$ and $L^{(-)}$ matrices in terms of $su_{q}(m\mid n)$ generators are presented. We also show that quantum…