Related papers: Supersymmetry and the Modular Double
For the family of the orthogonal quantum matrix algebras we investigate the structure of their characteristic subalgebras -- special commutative subalgebras, which for the subfamily of the reflection equation algebras appear to be central.…
The quantum group SL_q(2,R) at roots of unity is introduced by means of duality pairings with the quantum algebra U_q(sl(2,R)). Its irreducible representations are constructed through the universal T-matrix. An invariant integral on this…
We construct Drinfeld realisations for the quantum affine superalgebras associated with the osp(1|2n)^{(1)}, Sl(1|2n)^{(2)} and osp(2|2n)^{(2)} series of affine Lie superalgebras.
The quantum group analogue of the normalizer of SU(1,1) in SL(2,C) is an important and non-trivial example of a non-compact quantum group. The general theory of locally compact quantum groups in the operator algebra setting implies the…
We show how the supersymmetric properties of three dimensional black holes can be obtained algebraically. The black hole solutions are constructed as quotients of the supergroup $OSp(1|\,2;R)$ by a discrete subgroup of its isometry…
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…
Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and…
These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…
Representations of the quantum superalgebra U_q[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U_q[osp(1/2)] in which the…
We propose an N=4 supersymmetric quantum mechanics of a charged particle on a sphere in the background of Dirac magnetic monopole and study the system using the CP(1) model approach. We explicitly calculate the symmetry algebra taking the…
Second quantization is revisited and creation and annihilation operators are shown to be related, on the same footing both to the algebra ${\it h}(1)$, ${\underline {and}}$ to the superalgebra ${\it osp}(1|2)$ that are shown to be both…
The definitions and some properties (e.g. the Wigner-Eckart theorem, the fusion procedure) of covariant and contravariant q-tensor operators for quasitriangular quantum Lie algebras are formulated in the R-matrix language. The case of…
We compute the first differential cohomology of the orthosymplectic Lie superalgebra $\mathfrak{osp}(2|2)$ with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the…
The super-algebraic structure of a generalized version of the Jaynes-Cummings model is investigated. We find that a Z2 graded extension of the so(2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the…
We discuss the structure of the non-anticommutative N=2 non-linear sigma-model in two dimensions, constructing differential operators which implement the deformed supersymmetry generators and using them to reproduce the classical action. We…
We determine the exact global structure of the moduli space of $N{=}2$ supersymmetric $SO(n)$ and $\USp(2n)$ gauge theories with matter hypermultiplets in the fundamental representations, using the non-renormalization theorem for the Higgs…
We introduce a new kind of non-relativistic ${\cal N}{=}\,8$ supersymmetric mechanics, associated with worldline realizations of the supergroup $SU(2|2)$ treated as a deformation of flat ${\cal N}{=}\,8$, $d{=}1$ supersymmetry. Various…
The quantum supergroup OSPq(1|2n) is studied systematically. A Haar functional is constructed, and an algebraic version of the Peter - Weyl theory is extended to this quantum supergroup. Quantum homogeneous superspaces and quantum…
We derive the explicit form of the basic monodromy operator for the quantum loop superalgebra $\mathrm{U}_q(\mathcal{L}(\mathfrak{sl}_{2|1}))$. Two significant additional results emerge from this derivation: simple expressions for the…
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…