2,136 research outputs found
Modular realizations of hyperbolic Weyl groups
We study the recently discovered isomorphisms between hyperbolic Weyl groups and unfamiliar modular groups. These modular groups are defined over integer domains in normed division algebras, and we focus on the cases involving quaternions and octonions. We outline how to construct and analyse automorphic forms for these groups; their structure depends on the underlying arithmetic properties of the integer domains. We also give a new realization of the Weyl group W(E8) in terms of unit octavians and their automorphism group
Modular realizations of hyperbolic Weyl groups
We study the recently discovered isomorphisms between hyperbolic Weyl groups and unfamiliar modular groups. These modular groups are defined over integer domains in normed division algebras, and we focus on the cases involving quaternions and octonions. We outline how to construct and analyse automorphic forms for these groups; their structure depends on the underlying arithmetic properties of the integer domains. We also give a new realization of the Weyl group W(E8) in terms of unit octavians and their automorphism group
Labor Movements, Mainly in Eastern Europe
The main factors of labor movements, mainly in Eastern Europe, are considered in this paper. The influence
of economic indicators and peculiarities of economic development of the countries of the region in the current
migration situation in Europe as a whole has been studied. The analysis of the migration policy of the
countries of the European Union and individual countries is performed. The main tendencies of migration
flows of the population in the region and separate countries of Eastern Europe are revealed. General migration
problems as an integrational form of the existence of modern economies of the countries are
summarized
Remarks on E11 approach
We consider a few topics in approach to superstring/M-theory: even
subgroups ( orbifolds) of , n=11,10,9 and their connection to
Kac-Moody algebras; subgroup of and coincidence of one of
its weights with the weight of , known to contain brane charges;
possible form of supersymmetry relation in ; decomposition of
w.r.t. the and its square root at first few levels; particle orbit
of . Possible relevance of coadjoint orbits method is
noticed, based on a self-duality form of equations of motion in .Comment: Two references adde
Sugawara-type constraints in hyperbolic coset models
In the conjectured correspondence between supergravity and geodesic models on
infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the
constraints play a central role. We present a Sugawara-type construction in
terms of the E10 Noether charges that extends these constraints infinitely into
the hyperbolic algebra, in contrast to the truncated expressions obtained in
arXiv:0709.2691 that involved only finitely many generators. Our extended
constraints are associated to an infinite set of roots which are all imaginary,
and in fact fill the closed past light-cone of the Lorentzian root lattice. The
construction makes crucial use of the E10 Weyl group and of the fact that the
E10 model contains both D=11 supergravity and D=10 IIB supergravity. Our
extended constraints appear to unite in a remarkable manner the different
canonical constraints of these two theories. This construction may also shed
new light on the issue of `open constraint algebras' in traditional canonical
approaches to gravity.Comment: 49 page
Generalised holonomies and K(E9)
The involutory subalgebra K(E) of the affine Kac-Moody algebra E was recently shown to admit an infinite sequence of unfaithful representations of ever increasing dimensions arXiv:2102.00870. We revisit these representations and describe their associated ideals in more detail, with particular emphasis on two chiral versions that can be constructed for each such representation. For every such unfaithful representation we show that the action of K(E) decomposes into a direct sum of two mutually commuting (`chiral' and `anti-chiral') parabolic algebras with Levi subalgebra . We also spell out the consistency conditions for uplifting such representations to unfaithful representations of K(E). From these results it is evident that the holonomy groups so far discussed in the literature are mere shadows (in a Platonic sense) of a much larger structure
E10 and SO(9,9) invariant supergravity
We show that (massive) D=10 type IIA supergravity possesses a hidden rigid
SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional
reduction to one (time-like) dimension. We explicitly construct the associated
locally supersymmetric Lagrangian in one dimension, and show that its bosonic
sector, including the mass term, can be equivalently described by a truncation
of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a
decomposition of E10 under its so(9,9) subalgebra. This decomposition is
presented up to level 10, and the even and odd level sectors are identified
tentatively with the Neveu--Schwarz and Ramond sectors, respectively. Further
truncation to the level \ell=0 sector yields a model related to the reduction
of D=10 type I supergravity. The hyperbolic Kac--Moody algebra DE10, associated
to the latter, is shown to be a proper subalgebra of E10, in accord with the
embedding of type I into type IIA supergravity. The corresponding decomposition
of DE10 under so(9,9) is presented up to level 5.Comment: 1+39 pages LaTeX2e, 2 figures, 2 tables, extended tables obtainable
by downloading sourc
Representations of G+++ and the role of space-time
We consider the decomposition of the adjoint and fundamental representations
of very extended Kac-Moody algebras G+++ with respect to their regular A type
subalgebra which, in the corresponding non-linear realisation, is associated
with gravity. We find that for many very extended algebras almost all the A
type representations that occur in the decomposition of the fundamental
representations also occur in the adjoint representation of G+++. In
particular, for E8+++, this applies to all its fundamental representations.
However, there are some important examples, such as An+++, where this is not
true and indeed the adjoint representation contains no generator that can be
identified with a space-time translation. We comment on the significance of
these results for how space-time can occur in the non-linear realisation based
on G+++. Finally we show that there is a correspondence between the A
representations that occur in the fundamental representation associated with
the very extended node and the adjoint representation of G+++ which is
consistent with the interpretation of the former as charges associated with
brane solutions.Comment: 45 pages, 9 figures, 9 tables, te
COMMERCIAL FISHING RIGHTS ALLOCATION IN POST-APARTHEID SOUTH AFRICA: RECONCILING EQUITY AND STABILITY
No Abstract.African Journal of Marine Science Vol.25(1) 2003: pp. 25-3
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