Related papers: Tachyons and Representations of SO(2,3)

We construct a faithful categorical representation of an infinite Temperley-Lieb algebra on the periplectic analogue of Deligne's category. We use the corresponding combinatorics to classify thick tensor ideals in this periplectic Deligne…

Symmetric Space Sine-Gordon theories are two-dimensional massive integrable field theories, generalising the Sine-Gordon and Complex Sine-Gordon theories. To study their integrability properties on the real line, it is necessary to…

We construct the E theory analogue of the particles that transform under the Poincare group, that is, the irreducible representations of the semi-direct product of the Cartan involution subalgebra of E11 with its vector representation. We…

Let ${\mathcal F}_\lambda(\mathbb{S}^n)$ be the space of tensor densities on $\mathbb{S}^n$ of degree $\lambda$. We consider this space as an induced module of the nonunitary spherical series of the group $\mathrm{SO}_0(n+1,1)$ and classify…

We consider general linear superalgebra (type A) and tensor with Laurent polynomial ring in several variables. We then consider the universal central extension of this Lie superalgebra which we call toroidal superalgebra. We give a faithful…

We investigate how the matrix representation of SU(N) algebra approaches that of the Poisson algebra in the large N limit. In the adjoint representation, the (N^2-1) times (N^2-1) matrices of the SU(N) generators go to those of the Poisson…

In the present paper we construct all short representation of $so(3,2)$ with the $sl(2,\mathbb{C})$ symmetry made manifest due to the use of $sl(2,\mathbb{C})$ spinors. This construction has a natural connection to the spinor-helicity…

Solitons in two-dimensional quantum field theory exhibit patterns of degeneracies and associated selection rules on scattering amplitudes. We develop a representation theory that captures these intriguing features of solitons. This…

All Lie bialgebra structures for the (1+1)-dimensional centrally extended Schrodinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all of them come from a classical r-matrix, the complete family…

In this article, we clarify the link between the conformal (i.e. Weyl) correspondence from the Minkowski space to the de Sitter space and the conformal (i.e. SO(2,$d$)) invariance of the conformal scalar field on both spaces. We exhibit the…

Results are obtained on extending flat vector bundles or equivalently general representations from the fundamental group of S, a connected subsurface of the connected boundary of a compact, connected, oriented 3-dimensional manifold, to the…

We prove a version of the Poincare-Birkhoff-Witt theorem for the twisted quantized enveloping algebra U'_q(sp_2n). This is a subalgebra of U_q(gl_2n) and a deformation of the universal enveloping algebra U(sp_2n) of the symplectic Lie…

In this paper we present the solution to a longstanding problem of differential geometry: Lie's third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we…

We construct a massive non-abelian N= 1 SYM theory on R^3. This is achieved by using a non-local gauge and Poincare invariant mass term for gluons due to Nair. The underlying supersymmetry algebra is shown to be a non-central extension of…

This thesis studies the representation theory and linear structures of $\mathcal{Q}$-manifolds and higher Lie algebroids. We introduce differential graded modules (or for short DG-modules) of $\mathcal{Q}$-manifolds and the equivalent…

We continue our work on understanding Howe correspondences by using theta representations from p-adic groups to compact groups. We prove some results for unitary theta representations of compact groups with respect to the induction and…

We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these…

Using colored superanalysis and epsilon-Lie superalgebras, we build the minimal Poincare superalgebra in the case of the Z_n^3-grading. We then build a representation of this algebra, and the corresponding Poincare supergroup.

We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…

We study the Lie algebras of the covariant representations transforming the matter fields under the de Sitter isometries. We point out that the Casimir operators of these representations can be written in closed forms and we deduce how…