Related papers: Discrete U-duality Groups

Matched pairs of Lie groupoids and Lie algebroids are studied. Discrete Euler-Lagrange equations are written for the matched pairs of Lie groupoids. As such, a geometric framework to analyse a discrete system by decomposing it into two…

It is shown that the generators of two discrete Heisenberg-Weyl groups with irrational rotation numbers $\theta$ and $-1/ \theta$ generate the whole algebra $\cal B$ of bounded operators on $L_2(\bf R)$. The natural action of the modular…

We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of…

We discuss the topology of the symmetry groups appearing in compactified (super-)gravity, and discuss two applications. First, we demonstrate that for 3 dimensional sigma models on a symmetric space G/H with G non-compact and H the maximal…

We compute the group homology, the topological K-theory of the reduced C^*-algebra, the algebraic K-theory and the algebraic L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4.…

We provide a procedure for generating the irreducible representations of crystallography groups in any dimension. We also furnish a strategy to investigate the topology of the unitary dual of a crystallography group using sequences of…

In this paper we consider ultra-parallel complex hyperbolic triangle groups of type $[m_1,m_2,0]$, i.e. groups of isometries of the complex hyperbolic plane, generated by complex reflections in three ultra-parallel complex geodesics two of…

It has recently been shown that the full automorphism group of the Leech lattice, Conway's group Co_0, can be generated by 3 x 3 matrices over the octonions. We show such matrices are of type F_4 in E_{6(-26)}, the U-duality group for N=2,…

Discretized nonabelian gauge theories living on finite group spaces G are defined by means of a geometric action \int Tr F \wedge *F. This technique is extended to obtain discrete versions of the Born-Infeld action. The discretizations are…

We study aspects of Heterotic/F-theory duality for compactifications with Abelian discrete gauge symmetries. We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with n-sections, associated with the…

We present M-theory compactifications on $K_3 \times K_3$ with membranes near the $A_n$ or $D_n$ singularities of the $K_3$ spaces. By realizing each of these compactifications in two different ways as type I' models with 2- and 6-branes,…

When compactifying M- or type II string-theories on tori of indefinite space-time signature, their low energy theories involve sigma models on E_{n(n)}/H_n, where H_n is a not necessarily compact subgroup of E_{n(n)} whose complexification…

We present a 1-loop toroidal membrane winding sum reproducing the conjectured $M$-theory, four-graviton, eight derivative, $R^4$ amplitude. The $U$-duality and toroidal membrane world-volume modular groups appear as a Howe dual pair in a…

We develop methods to study the singularities of certain $G_2$ cones related to toric hyperkahler spaces and Einstein selfdual orbifolds. This allows us to determine the low energy gauge groups of chiral N=1 compactifications of M-theory on…

We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…

We classify all compact quantum groups whose C*-algebra sits inside that of the free unitary quantum groups $U_{N}^{+}$. In other words, we classify all discrete quantum subgroups of $\widehat{U}_{N}^{+}$, thereby proving a quantum variant…

We study structural properties and the harmonic analysis of discrete subgroups of the Euclidean group. In particular, we 1. obtain an efficient description of their dual space, 2. develop Fourier analysis methods for periodic mappings on…

Discrete quantum groups were introduced as duals of compact quantum groups by Podle\'s and Woronowicz in 1990. Shortly after, they were defined and studied intrinsically by Effros and Ruan, and by this author. In 1998, with the introduction…

The equations of motion of the massless sector of the two dimensional string theory, obtained by compactifying the heterotic string theory on an eight dimensional torus, is known to have an affine o(8,24) symmetry algebra generating an…

We develop a duality theory for multiplier Banach-Hopf algebras over a non-Archimedean field K. As examples, we consider algebras corresponding to discrete groups and zero-dimensional locally compact groups with K-valued Haar measure, as…