Positive Energy Representations, Holomorphic Discrete Series and Finite-Dimensional Irreps (2007)
Let G be a semi-simple non-compact Lie group with unitary lowest/highest weight representations. We consider explicitly the relation between three types of representations of G: positive energy...
Representations and characters of the Virasoro algebra and N=1 super-Virasoro algebras (2007)
We present the list of irreducible (generalized) highest weight modules over the Virasoro algebra and N=1 super-Virasoro algebras obtained as factor-modules of (generalized) Verma modules. We present...
Characters of the Unitarizable Highest Weight Modules over the N=2 Superconformal Algebras (2007)
The characters of the unitarizable highest weight modules over the N=2 superconformal algebras are presented. This is a slightly extended version of an Encyclopedia entry.
Higher Dimensional Multiparameter Unitary and Nonunitary Braid Matrices: Even Dimensions (2007)
Abdesselam, B., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
A class of $(2n)^2\times(2n)^2$ multiparameter braid matrices are presented for all $n$ $(n\geq 1)$. Apart from the spectral parameter $\theta$, they depend on $2n^2$ free parameters...
Invariant Differential Operators for Non-Compact Lie Groups: Parabolic Subalgebras (2007)
In the present paper we start the systematic explicit construction of invariant differential operators by giving explicit description of one of the main ingredients - the cuspidal parabolic...
Abdesselam, B., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We construct $(2n)^2\times (2n)^2$ unitary braid matrices $\hat{R}$ for $n\geq 2$ generalizing the class known for $n=1$. A set of $(2n)\times (2n)$ matrices $(I,J,K,L)$ are defined. $\hat{R}$ is...
q-Plane Wave Solutions of q-Weyl gravity (2007)
We give solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves.
On a "New" Deformation of GL(2) (2007)
Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We refute a recent claim in the literature of a "new" quantum deformation of GL(2).
Exotic Bialgebra S03: Representations, Baxterisation and Applications (2006)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation, which is not a deformation of the trivial, is considered. Its FRT dual algebra $s03_F$ is studied. The Baxterisation of...
Invariant Differential Operators and Characters of the AdS_4 Algebra (2005)
The aim of this paper is to apply systematically to AdS_4 some modern tools in the representation theory of Lie algebras which are easily generalised to the supersymmetric and quantum group settings...
Duality and Representations for New Exotic Bialgebras (2005)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic...
Duality for Exotic Bialgebras (2005)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
In the classification of Hietarinta, three triangular $4\\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find...
On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations (2005)
Aneva, B. L., Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
Combined $(q,h)$-deformations proposed by Kupershmidt and Ballesteros-Herranz-Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard $q$-deformation. We...
Exotic bialgebras : non-deformation quantum groups (2004)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
In the classification of solutions of the Yang--Baxter equation, there are solutions that are not deformations of the trivial solution (essentially the identity). We consider the algebras defined by...
Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry (2004)
We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long...
q-Conformal Invariant Equations and q-Plane Wave Solutions (2004)
We give new solutions of the quantum conformal deformations of the full Maxwell equations in terms of deformations of the plane wave. We study the compatibility of these solutions with the...
On the Unitarity of D=9,10,11 Conformal Supersymmetry (2004)
Dobrev, V. K., Miteva, A. M., Zhang, R. B., Zlatev, B. S.
We consider the unitarity of D=9,10,11 conformal supersymmetry using the recently established classification of the UIRs of the superalgebras osp(1|2n,R).
Positive Energy Unitary Irreducible Representations of the Superalgebras osp(1|2n,R) (2004)
We give the classification of the positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R).
New Generalized Verma Modules and Multilinear Intertwining Differential Operators (2003)
The present paper contains two interrelated developments. First, are proposed new generalized Verma modules. They are called k-Verma modules, k\in N, and coincide with the usual Verma modules for...
Duality and Representations for New Exotic Bialgebras (2003)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic...
Duality and Representations for New Exotic Bialgebras (2003)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic...
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We study the geometric aspects of two exotic bialgebras S03 and S14 introduced in math.QA/0206053. These bialgebras are obtained by the Faddeev-Reshetikhin-Takhtajan RTT prescription with...
Quantum Mechanics with Difference Operators (2002)
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth...
AdS/CFT Correspondence and Supersymmetry (2002)
We use the group-theoretic interpretation of the AdS/CFT correspondence which we proposed earlier in order to lift intertwining operators acting between boundary conformal representations to...
Duality and Representations for New Exotic Bialgebras (2002)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic...
Positive energy unitary irreducible representations of D=6 conformal supersymmetry (2002)
We give a constructive classification of the positive energy (lowest weight) unitary irreducible representations of the D=6 superconformal algebras osp(8*/2N). Our results confirm all but one of the...
Simple Applications of q-Bosons (2001)
Angelova, Maia, Dobrev, V. K., Frank, A.
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum...
Duality for Exotic Bialgebras (2001)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
In the classification of Hietarinta, three triangular $4\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find...
Duality for Exotic Bialgebras (2001)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
In the classification of Hietarinta, three triangular $4\\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find...
Duality for Exotic Bialgebras (2001)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
In the classification of Hietarinta, three triangular $4\\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find...
On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations (2000)
Aneva, B. L., Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
Combined $(q,h)$-deformations proposed by Kupershmidt and Ballesteros-Herranz-Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard $q$-deformation. We...
On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations (2000)
Aneva, B. L., Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
Combined $(q,h)$-deformations proposed by Kupershmidt and Ballesteros-Herranz-Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard $q$-deformation. We...
On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations (2000)
Aneva, B. L., Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
Combined $(q,h)$-deformations proposed by Kupershmidt and Ballesteros-Herranz-Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard $q$-deformation. We...
L\'evy Processes on $U_q(g)$ as Infinitely Divisible Representations (1999)
Dobrev, V. K., Franz, U., Schott, R.
L\'evy processes on bialgebras are families of infinitely divisible representations. We classify the generators of L\'evy processes on the compact forms of the quantum algebras $U_q(g)$, where $g$ is...
Intertwining Operator Realization of the AdS/CFT Correspondence (1998)
We give a group-theoretic interpretation of the AdS/CFT correspondence as relation of representation equivalence between representations of the conformal group describing the bulk AdS fields $\phi$...
Representations of the Generalized Lie Algebra sl(2)_q (1998)
We construct finite-dimensional irreducible representations of two quantum algebras related to the generalized Lie algebra $\ssll (2)_q$ introduced by Lyubashenko and the second named author. We...
Motivated by the fact that momentum observables which are modeled in a classical theory as difference quotients of functions are directly accessible to measurements, whereas differentials are...
Duality for the Jordanian Matrix Quantum Group $GL_{g,h}(2)$ (1997)
Aneva, B. L., Dobrev, V. K., Mihov, S. G.
We find the Hopf algebra $U_{g,h}$ dual to the Jordanian matrix quantum group $GL_{g,h}(2)$. As an algebra it depends only on the sum of the two parameters and is split in two subalgebras: $U'_{g,h}$...
q-Deformed Quantum Mechanical Evolution Equation via q-Deformed Schrödinger Algebra (1996)
We demonstrate how the 1-dimensional Schrodinger equation can be constructed using lowest weight modules and singular vectors of the (centrally extended) Schrodinger algebra in 1+1 spacetime...
Dobrev, V. K., Truini, P., Biedenharn, L. C.
A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and...
Representations of quantum groups and q-deformed invariant wave equations / (1995)
"Habilitationsschrift Clausthal 1994"--Cover.
q-difference intertwining operators for $U_q(sl(n))$: general setting and the case $n=3$ (1994)
We construct representations $\hat\pi_{\br}$ of the quantum algebra $U_q(sl(n))$ labelled by $n-1$ complex numbers $r_i$ and acting in the space of formal power series of $n(n-1)/2$ non-commuting...
Positive energy representations of the conformal quantum algebra (1993)
Dabrowski, L., Dobrev, V. K., Floreanini, R., Husain, V.
The positive-energy unitary irreducible representations of the $q$-deformed conformal algebra ${\cal C}_q = {\cal U}_q(su(2,2))$ are obtained by appropriate deformation of the classical ones. When...
Chair, N., Dobrev, V. K., Kanno, H.
We consider BRST quantized 2D gravity coupled to conformal matter with arbitrary central charge $c^M = c(p,q) < 1$ in the conformal gauge. We apply a Lian-Zuckerman $SO(2,\bbc)$ ($(p,q)$ - dependent)...