4,867 research outputs found
Equivariant map superalgebras
Suppose a group acts on a scheme and a Lie superalgebra
. The corresponding equivariant map superalgebra is the Lie
superalgebra of equivariant regular maps from to . We
classify the irreducible finite dimensional modules for these superalgebras
under the assumptions that the coordinate ring of is finitely generated,
is finite abelian and acts freely on the rational points of , and
is a basic classical Lie superalgebra (or ,
, if is trivial). We show that they are all (tensor products
of) generalized evaluation modules and are parameterized by a certain set of
equivariant finitely supported maps defined on . Furthermore, in the case
that the even part of is semisimple, we show that all such
modules are in fact (tensor products of) evaluation modules. On the other hand,
if the even part of is not semisimple (more generally, if
is of type I), we introduce a natural generalization of Kac
modules and show that all irreducible finite dimensional modules are quotients
of these. As a special case, our results give the first classification of the
irreducible finite dimensional modules for twisted loop superalgebras.Comment: 27 pages. v2: Section numbering changed to match published version.
Other minor corrections. v3: Minor corrections (see change log at end of
introduction
Masonry components
Masonry is a non-homogeneous material, composed of units and mortar, which can be of different types, with distinct mechanical properties. The design of both masonry units and mortar is based on the role of the walls in the building. Load-bearing walls relate to structural elements that bear mainly vertical loads, but can serve also to resist to horizontal loads. When a structural masonry building is submitted to in-plane and out-of-plane loadings induced by an earthquake for example, the masonry walls are the structural elements that ensure the global stability of the building. This means that the walls should have adequate mechanical properties that enable them to resist to different combinations of compressive, shear and tensile stresses.The boundary conditions influence the resisting mechanisms of the structural walls under in-plane loading and in a buildings the connection at the intersection walls are of paramount importance for the out-of-plane resisting mechanism. However, it is well established that the masonry mechanical properties are also relevant for the global mechanical performance of the structural masonry walls. Masonry units for load-bearing walls are usually laid so that their perforations are vertically oriented, whereas for partition walls, brick units with horizontal perforation are mostly adopted
Cluster algebras of type
In this paper we study cluster algebras \myAA of type . We solve
the recurrence relations among the cluster variables (which form a T--system of
type ). We solve the recurrence relations among the coefficients of
\myAA (which form a Y--system of type ). In \myAA there is a
natural notion of positivity. We find linear bases \BB of \myAA such that
positive linear combinations of elements of \BB coincide with the cone of
positive elements. We call these bases \emph{atomic bases} of \myAA. These
are the analogue of the "canonical bases" found by Sherman and Zelevinsky in
type . Every atomic basis consists of cluster monomials together
with extra elements. We provide explicit expressions for the elements of such
bases in every cluster. We prove that the elements of \BB are parameterized
by \ZZ^3 via their --vectors in every cluster. We prove that the
denominator vector map in every acyclic seed of \myAA restricts to a
bijection between \BB and \ZZ^3. In particular this gives an explicit
algorithm to determine the "virtual" canonical decomposition of every element
of the root lattice of type . We find explicit recurrence relations
to express every element of \myAA as linear combinations of elements of
\BB.Comment: Latex, 40 pages; Published online in Algebras and Representation
Theory, springer, 201
On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
The centrally extended su(2|2) superalgebra is an asymptotic symmetry of the
light-cone string sigma model on AdS5 x S5. We consider an evaluation
representation of the conventional Yangian built over a particular
16-dimensional long representation of the centrally extended su(2|2).
Interestingly, we find that S-matrices compatible with this evaluation
representation do not exist. On the other hand, by requiring centrally extended
su(2|2) invariance and explicitly solving the Yang-Baxter equation, we find a
scattering matrix for long-short representations of the Lie superalgebra. We
notice that this S-matrix is invariant under a different representation of
non-evaluation type, induced from the tensor product of short representations.
Our findings concern the conventional Yangian only, and are not applied to
possible algebraic extensions of the latter.Comment: Version accepted for publication in JHE
Separatrix splitting at a Hamiltonian bifurcation
We discuss the splitting of a separatrix in a generic unfolding of a
degenerate equilibrium in a Hamiltonian system with two degrees of freedom. We
assume that the unperturbed fixed point has two purely imaginary eigenvalues
and a double zero one. It is well known that an one-parametric unfolding of the
corresponding Hamiltonian can be described by an integrable normal form. The
normal form has a normally elliptic invariant manifold of dimension two. On
this manifold, the truncated normal form has a separatrix loop. This loop
shrinks to a point when the unfolding parameter vanishes. Unlike the normal
form, in the original system the stable and unstable trajectories of the
equilibrium do not coincide in general. The splitting of this loop is
exponentially small compared to the small parameter. This phenomenon implies
non-existence of single-round homoclinic orbits and divergence of series in the
normal form theory. We derive an asymptotic expression for the separatrix
splitting. We also discuss relations with behaviour of analytic continuation of
the system in a complex neighbourhood of the equilibrium
Growth of Inclined GaAs Nanowires by Molecular Beam Epitaxy: Theory and Experiment
The growth of inclined GaAs nanowires (NWs) during molecular beam epitaxy (MBE) on the rotating substrates is studied. The growth model provides explicitly the NW length as a function of radius, supersaturations, diffusion lengths and the tilt angle. Growth experiments are carried out on the GaAs(211)A and GaAs(111)B substrates. It is found that 20° inclined NWs are two times longer in average, which is explained by a larger impingement rate on their sidewalls. We find that the effective diffusion length at 550°C amounts to 12 nm for the surface adatoms and is more than 5,000 nm for the sidewall adatoms. Supersaturations of surface and sidewall adatoms are also estimated. The obtained results show the importance of sidewall adatoms in the MBE growth of NWs, neglected in a number of earlier studies
The conformal current algebra on supergroups with applications to the spectrum and integrability
We compute the algebra of left and right currents for a principal chiral
model with arbitrary Wess-Zumino term on supergroups with zero Killing form. We
define primary fields for the current algebra that match the affine primaries
at the Wess-Zumino-Witten points. The Maurer-Cartan equation together with
current conservation tightly constrain the current-current and current-primary
operator product expansions. The Hilbert space of the theory is generated by
acting with the currents on primary fields. We compute the conformal dimensions
of a subset of these states in the large radius limit. The current algebra is
shown to be consistent with the quantum integrability of these models to
several orders in perturbation theory.Comment: 45 pages. Minor correction
Formal Hecke algebras and algebraic oriented cohomology theories
In the present paper we generalize the construction of the nil Hecke ring of
Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology
theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's
K_0, connective K-theory, elliptic cohomology, and algebraic cobordism. The
resulting object, which we call a formal (affine) Demazure algebra, is
parameterized by a one-dimensional commutative formal group law and has the
following important property: specialization to the additive and multiplicative
periodic formal group laws yields completions of the nil Hecke and the 0-Hecke
rings respectively. We also introduce a deformed version of the formal (affine)
Demazure algebra, which we call a formal (affine) Hecke algebra. We show that
the specialization of the formal (affine) Hecke algebra to the additive and
multiplicative periodic formal group laws gives completions of the degenerate
(affine) Hecke algebra and the usual (affine) Hecke algebra respectively. We
show that all formal affine Demazure algebras (and all formal affine Hecke
algebras) become isomorphic over certain coefficient rings, proving an analogue
of a result of Lusztig.Comment: 28 pages. v2: Some results strengthened and references added. v3:
Minor corrections, section numbering changed to match published version. v4:
Sign errors in Proposition 6.8(d) corrected. This version incorporates an
erratum to the published versio
D3/D7 Quark-Gluon Plasma with Magnetically Induced Anisotropy
We study the effects of the temperature and of a magnetic field in the setup
of an intersection of D3/D7 branes, where a large number of D7 branes is
smeared in the transverse directions to allow for a perturbative solution in a
backreaction parameter. The magnetic field sources an anisotropy in the plasma,
and we investigate its physical consequences for the thermodynamics and energy
loss of particles probing the system. In particular we comment on the
stress-energy tensor of the plasma, the propagation of sound in the directions
parallel and orthogonal to the magnetic field, the drag force of a quark moving
through the medium and jet quenching.Comment: 29 pages + appendices, 5 figures. v2 Version to appear in JHEP, with
minor revisions, references added and typos correcte
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