相关论文: Representation of the Quantum Plane, its Quantum D…

In the first part of this paper, we implement the multiplier algebra of the dual of an algebraic quantum group (A,Delta) as a space of linear functionals on A. In the second part, we construct the universal corepresentation of (A,Delta) and…

This paper is devoted to the representation theory of quantum coordinate algebra $\mathbb{C}_q[G]$, for a semisimple Lie group $G$ and a generic parameter $q$. By inspecting the actions of normal elements on tensor modules, we generalize a…

Pairing between the universal enveloping algebra $U_q(sl(2))$ and the algebra of functions over $SL_q(2)$ is obtained in explicit terms. The regular representation of the quantum double is constructed and investigated. The structure of the…

We find all unitary representations of the quantum "ax+b" group. It turns out that this quantum group is selfdual in the sense that all unitary representations are 'numbered' by elements of the same group. Moreover, we discover the formula…

The two-parametric quantum superalgebra $U_{p,q}[gl(2/2)]$ and its induced representations are considered. A method for constructing all finite-dimensional irreducible representations of this quantum superalgebra is also described in…

The structure and representations of the quantum general linear supergroup GLq(m|n) are studied systematically by investigating the Hopf superalgebra Gq of its representative functions. Gq is factorized into $Gq^{\pi} Gq^{\bar\pi}$, and a…

In this paper a new quasi-triangular Hopf algebra as the quantum double of the Heisenberg-Weyl algebra is presented.Its universal R-matrix is built and the corresponding representation theory are studied with the explict construction for…

We introduce $*$-structures on braided groups and braided matrices. Using this, we show that the quantum double $D(U_q(su_2))$ can be viewed as the quantum algebra of observables of a quantum particle moving on a hyperboloid in q-Minkowski…

We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…

The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical)…

A review of the multiparametric linear quantum group GL_qr(N), its real forms, its dual algebra U(gl_qr(N)) and its bicovariant differential calculus is given in the first part of the paper. We then construct the (multiparametric) linear…

It is shown that all important features of a $\mathrm{C}^*$-algebraic quantum group $(A,\Delta)$ defined by a modular multiplicative $W$ depend only on the pair $(A,\Delta)$ rather than the multiplicative unitary operator $W$. The proof is…

The Kronecker coefficient g_{\lambda \mu \nu} is the multiplicity of the GL(V)\times GL(W)-irreducible V_\lambda \otimes W_\mu in the restriction of the GL(X)-irreducible X_\nu via the natural map GL(V)\times GL(W) \to GL(V \otimes W),…

Geiss-Leclerc-Schroer defined the cluster algebra structure on the coordinate ring $C[N(w)]$ of the unipotent subgroup, associated with a Weyl group element $w$ and they proved cluster monomials are contained in Lusztig's dual semicanonical…

The double quantum groups are the Hopf algebras underlying the complex quantum groups of which the simplest example is the quantum Lorentz group. They are non- standard quantizations of the double group $G \times G$. We construct a…

We use the crystallised $C^*$-algebra $C(SU_{q}(2))$ at $q=0$ to obtain a unitary that gives an approximate equivalence involving the GNS representation on the $L^{2}$ space of the Haar state of the quantum $SU(2)$ group and the direct…

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…

We showed that there is a complete analogue of a representation of the quantum plane B_q where |q|=1, with the classical ax+b group. We showed that the Fourier Transform of the representation of B_q on H=L^2(R) has a limit (in the dual…

We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is…

We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2+1 dimensions, motivated by its role as a deformed Poincar\'e symmetry and symmetry algebra in (2+1)-dimensional quantum gravity. We…