We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of SO(1, n). As a result we prove that for any even dimension n there exists a unique compact arithmetic hyperbolic n-orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an e...

Following De Ruiter (2000), I propose that there is no such thing as a lexical affiliate for every gesture. I suggest interpreting gestures by their conceptual affiliates. The existence of conceptual rather than lexical gesture affiliates is supported by empirical data from a perception study with German native speakers. They linked gestures in video clips without sound to their accompanying sp...

The analog of the principal SO(3) subalgebra of a finite dimensional simple Lie algebra can be defined for any hyperbolic Kac Moody algebra g(A) associated with a symmetrizable Cartan matrix A, and coincides with the non-compact group SO(1, 2). We exhibit the decomposition of g(A) into representations of SO(1, 2); with the exception of the adjoint SO(1, 2) algebra itself, all of these represent...

Let Γ be a torsion-free lattice in SO0(3, 1), and let M = Γ\H3 be the corresponding hyperbolic 3-manifold. It is wellknown that in the presence of a closed, embedded, totallygeodesic surface in M , the canonical flat conformal structure on M can be deformed via the bending construction. Equivalently, the lattice Γ admits non-trivial deformations into SO0(4, 1). We present a new construction of ...

We construct the N = 1 supergravity analog of the Green-Schwarz and heterotic superstring theories in 10D. We find the SO(8) theory previously found by compactification of 10D on K3. We also find eleven G 2 × G 2 theories, two with symmetric matter content. It is not obvious how tenof the G 2 × G 2 theories can be gotten from 10D. Ten-dimensional superstrings [1], [2], [3], [4] are one of the m...

The analog of the principal SO(3) subalgebra of a finite dimensional simple Lie algebra can be defined for any hyperbolic Kac Moody algebra g(A) associated with a symmetrizable Cartan matrix A, and coincides with the non-compact algebra SO(1, 2). We exhibit the decomposition of g(A) into representations of SO(1, 2); with the exception of the adjoint SO(1, 2) algebra itself, all of these represe...

When making a mistake, individuals are willing to apologize to secure further cooperation, even if the apology is costly. Similarly, individuals arrange commitments to guarantee that an action such as a cooperative one is in the others’ best interest, and thus will be carried out to avoid eventual penalties for commitment failure. Hence, both apology and commitment should go side by side in beh...