Related papers: The Minimal Unitary Representation of E_8(8)

For a locally compact group $G$, we show that it is possible to present the class of continuous unitary representations of $G$ as an elementary class of metric structures, in the sense of continuous logic. More precisely, we show how…

A representation field for a non-maximal order H in a central simple algebra A is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders representing H. In our previous work we…

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 conjectures of Minwalla (for N=1,2) on…

It is well known that there is a unique $Spin(9)$-invariant 8-form on the octonionic plane that naturally yields a canonical differential 8-form on any Riemannian manifold with a weak $Spin(9)$-structure. Over the decades, this invariant…

By analogy with the real and complex affine groups, whose unitary irreducible representations are used to define the one and two-dimensional continuous wavelet transforms, we study here the quaternionic affine group and construct its…

In this paper we present new formulas, which represent commutators and anticommutators of Clifford algebra elements as sums of elements of different ranks. Using these formulas we consider subalgebras of Lie algebras of pseudounitary…

In this paper various representations of the exceptional Lie algebra G_2 are investigated in a purely algebraic manner, and multi-boson/multi-fermion realizations are obtained. Matrix elements of the master representation, which is defined…

We discuss the possibility of very regular subgroups of a Lie group, in presence of an index figure. Further, representations that reduce action to a very regular boundary.

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 (unitary lowest weight)representations,…

We ask when it is possible to construct arbitrary unitary multiplets of the superconformal algebra with eight Poincar\'e supercharges that are compatible with locality from (continuous deformations of) representations in free field…

We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…

We give upper bounds for the number of irreducible representations of dimension at most n for a compact semisimple Lie group. In particular, we prove that there are at most n irreducible representations of dimension at most n for a simple…

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 $G$ be a simple algebraic group over an algebraically closed field $k$, where $\mathrm{char}\, k$ is either 0 or a good prime for $G$. We consider the modality $\mathrm{mod}(B : \mathfrak u)$ of the action of a Borel subgroup $B$ of $G$…

In this note we show that the representation of the additive group of the Hilbert space $L^2([0,1],\R)$ on $L^2([0,1],\C)$ given by the multiplication operators $\pi(f) := e^{if}$ is continuous but its space of smooth vectors is trivial.…

We consider a straightforward extension of the 4-dimensional spacetime $M_4$ to the space of extended events associated with strings/branes, corresponding to points, lines, areas, 3-volumes, and 4-volumes in $M_4$. All those objects can be…

A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where…

The final version of a new approach to quantum theory is formulated in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to…

A minimal permutation representation of a finite group G is a faithful G-set with the smallest possible size. We study the structure of such representations and show that for certain groups they may be obtained by a greedy construction. In…

Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of the fundamental group of U with certain restrictions related to the divisor. We show that…