相关论文: A q-Analogue of the embedding chain $U(6) \supset …

A natural embedding $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$ for the corresponding quantum algebras is constructed through the appropriate comultiplication on the generators of each of the $A_{m-1}$ and $A_{n-1}$ algebras. The above…

An analog of the minimal unitary series representations for the deformed Virasoro algebra is constructed using vertex operators of the quantum affine algebra $U_q(\hat{sl}_2)$. A similar construction is proposed for the elliptic algebra…

A q-analogue of the gl_3 Drinfel'd-Sokolov hierarchy is proposed as a reduction of the q-KP hierarchy. Applying a similarity reduction and a q-Laplace transformation to the hierarchy, one can obtain the q-Painleve VI equation proposed by…

Various forms of the $q$-boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator. Both the one-component and the multicomponent $q$-bosons are discussed. As a byproduct, we obtain a new…

The new method of q-bosonization for quantum groups based on the Gauss decomposition of a transfer matrix of generators is suggested. The simplest example of the quantum group $GL_q(2)$ is considered in some details.

We provide an alternative approach to the Faddeev-Reshetikhin-Takhtajan presentation of the quantum group U_q(g), with L-operators as generators and relations ruled by an R-matrix. We look at U_q(g) as being generated by the quantum Borel…

The quantum algebra suq(2) is introduced as a deformation of the ordinary Lie algebra su(2). This is achieved in a simple way by making use of $q$-bosons. In connection with the quantum algebra suq(2), we discuss the q-analogues of the…

Attention is focused on q-deformed quantum algebras with physical importance, i.e. $U_{q}(su_{2})$, $U_{q}(so_{4})$ and q-deformed Lorentz algebra. The main concern of this article is to assemble important ideas about these symmetry…

Nonstandard q-deformed algebras U'_q(so_n), proposed a decade ago for the needs of representation theory, essentially differ from the standard Drinfeld-Jimbo quantum deformation of the algebras U(so_n) and possess with regard to the latter…

We derive a $q$-analogue of the matrix sixth Painlev\'e system via a connection-preserving deformation of a certain Fuchsian linear $q$-difference system. In specifying the linear $q$-difference system, we utilize the correspondence between…

We give explicit formulas for the generators of $q$-deformed W-algebras associated to Lie algebras $D_n, E_6$ and $G_2$, and compute the Poisson brackets between the generators.

A corrigendum of a former result on semisimplicity of the category of integrable modules of a q-boson algebra is given with a counter example.

We construct a subalgebra of the Hecke algebra of type A. This is a generalization of the group algebra of the alternating groups. All the equivalent classes of irreducible representations of the subalgebra and the q-analogue of the…

We give explicit expression of recurrency formulae of canonical realization for quantum enveloping algebras $U_{q}(sl(n+1,C))$. In these formulas the generators of the algebra $U_{q}(sl(n+1,C))$ are expressed by means of n-canonical q-boson…

Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…

A mapping between the operators of the bosonic oscillator and the Lorentz rotation and boost generators is presented. The analog of this map in the $q$-deformed regime is then applied to $q$-deformed bosonic oscillators to generate a…

Basic idea presented in Parts (I)-(III) for the deformed boson scheme is applied to the case of the su(2)- and su(1,1)-algebras for describing many-body systems consisting of four kinds of boson operators. A possible form of the coherent…

We classify the quantum numbers of the extra $U(1)'$ symmetries contained in $E_6$. In particular, we categorize the cases with rational charges and present the full list of models which arise from the chains of the maximal subgroups of…

An alternative to the Chevalley description of Lie algebra sl(n+1), of its universal enveloping algebra U[sl(n+1)] and of its q-deformed analogue U_q[sl(n+1)] in terms of generators, called creation and annihilation generators (CAGs), and…

Recently, the concept of a D-analogue was introduced by the author. This is a Dirichlet series analogue for the already known and well researched hypergeometric q-series. we consider the D-analogues of the q-binomial coefficients, and a…