Related papers: On representations of $U'_qso_n$
We describe properties of the nonstandard q-deformation U'_q(so_n) of the universal enveloping algebra U(so_n) of the Lie algebra so_n which does not coincide with the Drinfeld--Jimbo quantum algebra U_q(so_n). In particular, it is shown…
A classification of finite dimensional irreducible representations of the nonstandard $q$-deformation $U'_q(so_n)$ of the universal enveloping algebra $U(so(n, C))$ of the Lie algebra $so(n, C)$ (which does not coincides with the…
The aim of this paper is to give a complete classification of irreducible finite dimensional representations of the nonstandard q-deformation U'_q(so(n)) (which does not coincide with the Drinfeld-Jimbo quantum algebra U_q(so(n)) of the…
We describe properties of the nonstandard q-deformation $U'_q({\rm so}_n)$ of the universal enveloping algebra $U({\rm so}_n)$ of the Lie algebra ${\rm so}_n$ which does not coincide with the Drinfeld--Jimbo quantum algebra $U_q({\rm…
The nonstandard q-deformation $U'_q({\rm so}_n)$ of the universal enveloping algebra $U({\rm so}_n)$ has irreducible finite dimensional representations which are a q-deformation of the well-known irreducible finite dimensional…
The aim of this paper is to announce the results on irreducible nonclassical type representations of the nonstandard q-deformations U'_q(so_n), U_q(iso_n) and U'_q(so_{n,1}) of the universal enveloping algebras of the Lie algebras so(n,C),…
We study the nonstandard $q$-deformation $U'_q({\rm so}_4)$ of the universal enveloping algebra $U({\rm so}_4)$ obtained by deforming the defining relations for skew-symmetric generators of $U({\rm so}_4)$. This algebra is used in quantum…
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…
The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…
The main aim of this paper is to give classes of irreducible infinite dimensional representations and of irreducible $*$-representations of the q-deformed algebra $U'_q(so_{2,2})$ which is a real form of the non-standard deformation…
For the nonstandard $q$-deformed algebras $U_q(so_n)$, defined recently in terms of trilinear relations for generating elements, most general finite dimensional irreducible representations directly corresponding to those of nondeformed…
The Verma modules over the quantum groups $\mathrm U_q(\mathfrak{gl}_{l + 1})$ for arbitrary values of $l$ are analysed. The explicit expressions for the action of the generators on the elements of the natural basis are obtained. The…
A new 2-parameter quadratic deformation of the quantum oscillator algebra and its 1-parameter deformed Heisenberg subalgebra are considered. An infinite dimensional Fock module representation is presented which at roots of unity contains…
Noncompact forms of the Drinfeld-Jimbo quantum groups U_q(g) with (H_i)* = H_i, (X_i^{+-})* = s_i X_i^{-+} for s_i= +-1 are studied at roots of unity. This covers g = so(n,2p), su(n,p), so*(2l), sp(n,p), sp(l,R), and exceptional cases.…
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…
Quantum groups in general and the quantum Anti-de Sitter group $U_q(so(2,3))$ in particular are studied from the point of view of quantum field theory. We show that if $q$ is a suitable root of unity, there exist finite-dimensional, unitary…
The tensor product of vector and arbitrary representations of the nonstandard q-deformation U'_q(so(n)) of the universal enveloping algebra U(so(n)) of Lie algebra so(n) is defined. The Clebsch-Gordan coefficients of tensor product of…
We study irreducible unitary \reps of $U_q(SO(2,1))$ and $U_q(SO(2,3))$ for $q$ a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all classical one-particle representations with integral weights are…
Unitary principal series representations of the conformal group appear in the dS/CFT correspondence. These are infinite dimensional irreducible representations, without highest weights. In earlier work of Guijosa and the author it was shown…
q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…