Related papers: The smallest quantum Mackey deformation
The representation theory of the quantum group su$_q(2)$ is used to introduce $q$-analogues of the Wigner rotation matrices, spherical functions, and Legendre polynomials. The method amounts to an extension of variable separation from…
We construct a local deformation problem for residual Galois representations $\bar{\rho}$ valued in an arbitrary reductive group $\hat{G}$ which we use to develop a variant of the Taylor-Wiles method. Our generalization allows Taylor-Wiles…
Earlier we have proposed new $q$ - Maxwell equations which are the first members of an infinite new hierarchy of $q$ - difference equations. We have used an indexless formulation in which all indices are traded for two conjugate variables,…
We revisit the procedure of deformation of $C^*$-algebras via coactions of locally compact groups and extend the methods to cover deformations for maximal, reduced, and exotic coactions for a given group $G$ and circle-valued Borel…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
Let $\L_m$ be the scheme of the laws defined by the identities of Jacobi on $\K^m$. The local studies of an algebraic Lie algebra $\g=\mathrm{R}\ltimes\n$ in $\L_m$ and its nilpotent part $\n$ in the scheme $\L_n^{\mathrm{R}}$ of…
We propose a new structure ${\cal U}^{r}_{\displaystyle{q}}(sl(2)) $. This is realized by multiplying $\delta$ ($q=e^{\delta}$, $\delta\in \CC$) by $\theta$, where $\theta$ is a real nilpotent -paragrassmannian- variable of order $r$…
A $q$-deformed free scalar relativistic particle is discussed in the framework of the BRST formalism. The $q$-deformed local gauge symmetry and reparametrization invariance of the first-order Lagrangian have been exploited for the BRST…
Cayley's theorem tells us that all groups $\mathbf{G}$ occur as subgroups of the group of automorphisms over some set $X$. In this paper we consider a `sort-of' converse to this question: given a set $X$ and some transformation group…
We show that the deformation theory of Fr\'echet algebras for actions of K\"ahlerian Lie groups developed by two of us, leads in a natural way to examples of non-compact locally compact quantum groups. This is achieved by constructing a…
Quantum superalgebras $su_{q}(m\mid n)$ are studied in the framework of $R$-matrix formalism. Explicit parametrization of $L^{(+)}$ and $L^{(-)}$ matrices in terms of $su_{q}(m\mid n)$ generators are presented. We also show that quantum…
We introduce the analogue of the metric tensor in case of $q$-deformed differential calculus. We analyse the consequences of the existence of such metric, showing that this enforces severe restrictions on the parameters of the theory. We…
In this article we review the main results of the earlier papers [I. Penkov, K. Styrkas, Tensor representations of infinite-dimensional root-reductive Lie algebras, in Developments and Trends in Infinite-Dimensional Lie Theory, Progress in…
Quantum groups have been widely explored as a tool to encode possible nontrivial generalisations of reference frame transformations, relevant in quantum gravity. In quantum information, it was found that the reference frames can be…
In our paper arXiv:1701.03146 we established, for every simply-laced Lie algebra g, a canonical isomorphism between the spaces of deformed conformal blocks of the deformed W-algebra and the quantum affine algebra corresponding to g, which…
This note is an overview of the Poisson sigma model (PSM) and its applications in deformation quantization. Reduction of coisotropic and pre-Poisson submanifolds, their appearance as branes of the PSM, quantization in terms of L-infinity…
Quantum de Rham complexes on the quantum plane and the quantum group itself are constructed for the Zakrewski deformation of $ Fun ( SL(2)) $. As a by-product a new deformation of the two dimensional Heisenberg algeb ra is constructed which…
In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
We study representations of the classical infinite dimensional real simple Lie groups $G$ induced from factor representations of minimal parabolic subgroups $P$. This makes strong use of the recently developed structure theory for those…