Related papers: Irreducible representations of E theory
Diaconescu, Moore and Witten have shown that the topological part of the M-theory partition function is an invariant of an E8 gauge bundle over the 11-dimensional bulk. This presents a puzzle as an 11d gauge theory cannot exhibit linearly…
In this thesis we study algebraic structures in M-theory, in particular the exceptional Lie algebras arising in dimensional reduction of its low energy limit, eleven-dimensional supergravity. We focus on e8 and its infinite-dimensional…
For an arbitrary finite monoid $M$ and subgroup $K$ of the unit group of $M$, we prove that there is a bijection between irreducible representations of $M$ with nontrivial $K$-fixed space and irreducible representations of $\mathcal{H}_K$,…
Non-trivial extensions of the three dimensional Poincar\'e algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three dimensional generalizations of fractional supersymmetry of order…
We extend a recently proposed formulation of dual gravity to the case of eleven-dimensional supergravity. The supersymmetric action corresponding to this alternative formulation is given, and it is shown that it leads to a set of…
We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…
A four dimensional non-trivial extension of the Poincar\'e algebra different from supersymmetry is explicitly studied. Representation theory is investigated and an invariant Lagrangian is exhibited. Some discussion on the Noether theorem is…
In this paper we study eleven-dimensional supergravity in its most general form. This is done by implementing manifest supersymmetry (and Lorentz invariance) through the use of the geometric (torsion and curvature) superspace Bianchi…
We show that the commonly considered half BPS solutions of eleven dimensional supergravity and the ten dimensional type II theories, when expressed in terms of $E_{11}$ group elements, take the universal form $\exp(-{1\over 2}ln N…
Let $G$ be a finite group, $H$ be a normal subgroup of prime index $p$. Let $F$ be a field of either characteristic $0$ or prime to $|G|$. Let $\eta$ be an irreducible $F$-representation of $H$. If $F$ is an algebraically closed field of…
We review the often forgotten fact that gravitation theories invariant under local de Sitter, anti-de Sitter or Poincare transformations can be constructed in all odd dimensions. These theories belong to the Chern-Simons family and are…
By solving a set of recursion relations for the matrix elements of the ${\cal U}_h(sl(2))$ generators, the finite dimensional highest weight representations of the algebra were obtained as factor representations. Taking a nonlinear…
We investigate the most general N=1 graded extension of the Poincare algebra, and find the corresponding supersymmetry transformations and the associated superspaces. We find that the supersymmetry for which {Q,Q} = P is not special, and in…
We study families of self-adjoint operators with given spectra whose sum is a scalar operator. Such families are $*$-representations of certain algebras which can be described in terms of graphs and positive functions on them. The main…
We study the lowest dimensional typical and atypical representations of SU(5/3) superalgebra as a possible unified gauge theory having a natural SU(5) subalgebra with SU(3) extra structure, which will be used to accommodate three…
A reference frame on a set $M$ is given by a 3-dimensional euclidean space $E$, a function from $M$ to $E$, a 1-dimensional affine space $A$ and a function from $M$ to $A$. The definition allows an intuitive and coordinate-free formulation…
We investigate a family of (reducible) representations of Artin's braid groups corresponding to a specific solution to the Yang-Baxter equation. The images of the braid groups under these representations are finite groups, and we identify…
Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…
The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…
We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…