6,498 research outputs found
Analogues of Weyl's formula for reduced enveloping algebras
In this note we study simple modules for a reduced enveloping algebra
U_chi(g) in the critical case when chi element of g^* is ``nilpotent''. Some
dimension formulas computed by Jantzen suggest modified versions of Weyl's
dimension formula, based on certain reflecting hyperplanes for the affine Weyl
group which might be associated to Kazhdan--Lusztig cells.Comment: AMS-LaTeX, 10 pages, 2 figure
Majorana meets Coxeter: Non-Abelian Majorana Fermions and Non-Abelian Statistics
We discuss statistics of vortices having zero-energy non-Abelian Majorana
fermions inside them. Considering the system of multiple non-Abelian vortices,
we derive a non-Abelian statistics that differs from the previously derived
non-Abelian statistics. The new non-Abelian statistics presented here is given
by a tensor product of two different groups, namely the non-Abelian statistics
obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter
group is a symmetric group related to the symmetry of polytopes in a
high-dimensional space. As the simplest example, we consider the case in which
a vortex contains three Majorana fermions that are mixed with each other under
the SO(3) transformations. We concretely present the representation of the
Coxeter group in our case and its geometrical expressions in the
high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.Comment: 6 pages, 4 figures, references added, published versio
A New Multiplicity Formula for the Weyl Modules of Type A
A monomial basis and a filtration of subalgebras for the universal enveloping
algebra of a complex simple Lie algebra of type is given
in this note. In particular, a new multiplicity formula for the Weyl module
of is obtained in this note.Comment: 13 page
Antilinear deformations of Coxeter groups, an application to Calogero models
We construct complex root spaces remaining invariant under antilinear
involutions related to all Coxeter groups. We provide two alternative
constructions: One is based on deformations of factors of the Coxeter element
and the other based on the deformation of the longest element of the Coxeter
group. Motivated by the fact that non-Hermitian Hamiltonians admitting an
antilinear symmetry may be used to define consistent quantum mechanical systems
with real discrete energy spectra, we subsequently employ our constructions to
formulate deformations of Coxeter models remaining invariant under these
extended Coxeter groups. We provide explicit and generic solutions for the
Schroedinger equation of these models for the eigenenergies and corresponding
wavefunctions. A new feature of these novel models is that when compared with
the undeformed case their solutions are usually no longer singular for an
exchange of an amount of particles less than the dimension of the
representation space of the roots. The simultaneous scattering of all particles
in the model leads to anyonic exchange factors for processes which have no
analogue in the undeformed case.Comment: 32 page
Recommended from our members
A Dense Reference Network for Mass-Market Centimeter-Accurate Positioning
The quality of atmospheric corrections provided
by a dense reference network for centimeter-accurate carrierphase
differential GNSS (CDGNSS) positioning is investigated.
A dense reference network (less than 20 km inter-station distance)
offers significant benefits for mass-market users, enabling lowcost
(including single-frequency) CDGNSS positioning with rapid
integer ambiguity resolution. Precise positioning on a massmarket
platform would significantly influence the world economy,
ushering in a host of consumer-focused applications such as
globally-registered augmented and virtual reality and improved
all-weather safety and efficiency for intelligent transportation
systems, applications which have so far been hampered by the
several-meter-level errors in standard GNSS positioning. This
contribution examines CDGNSS integer ambiguity resolution
performance in terms of network correction uncertainty, and
network correction uncertainty, in turn, in terms of network
density. It considers the total error in network corrections: a
sum of ionospheric, tropospheric, and reference station multipath
components. The paper’s primary goal is to identify the network
density beyond which mass-market users would see no further
significant improvement in ambiguity resolution performance. It
finishes by describing development and deployment of a low-cost
dense reference network in Austin, Texas.Aerospace Engineering and Engineering Mechanic
A subsystem-independent generalization of entanglement
We introduce a generalization of entanglement based on the idea that
entanglement is relative to a distinguished subspace of observables rather than
a distinguished subsystem decomposition. A pure quantum state is entangled
relative to such a subspace if its expectations are a proper mixture of those
of other states. Many information-theoretic aspects of entanglement can be
extended to the general setting, suggesting new ways of measuring and
classifying entanglement in multipartite systems. By going beyond the
distinguishable-subsystem framework, generalized entanglement also provides
novel tools for probing quantum correlations in interacting many-body systems.Comment: 5 pages, 1 encapsulated color figure, REVTeX4 styl
Unveiling Sources of Heating in the Vicinity of the Orion BN/KL Hot Core as Traced by Highly Excited Inversion Transitions of Ammonia
Using the Expanded Very Large Array, we have mapped the vicinity of the Orion
BN/KL Hot Core with sub-arcsecond angular resolution in seven metastable
inversion transitions of ammonia: (J,K)=(6,6) to (12,12). This emission comes
from levels up to 1500 K above the ground state, enabling identification of
source(s) responsible for heating the region. We used this multi-transition
dataset to produce images of the rotational/kinetic temperature and the column
density of ammonia for ortho and para species separately and on a
position-by-position basis. We find rotational temperature and column density
in the range 160-490 K and (1-4)x10^17 cm^-2, respectively. Our
spatially-resolved images show that the highest (column) density and hottest
gas is found in a northeast-southwest elongated ridge to the southeast of
Source I. We have also measured the ortho-para ratio of ammonia, estimated to
vary in the range 0.9-1.6. Enhancement of ortho with respect to para and the
offset of hot ammonia emission peaks from known (proto)stellar sources provide
evidence that the ammonia molecules have been released from dust grains into
the gas-phase through the passage of shocks and not by stellar radiation. We
propose that the combined effect of Source I's proper motion and its
low-velocity outflow impinging on a pre-existing dense medium is responsible
for the excitation of ammonia and the Orion Hot Core. Finally, we found for the
first time evidence of a slow (5 km/s) and compact (1000 AU) outflow towards
IRc7.Comment: To appear in Astrophysical Journal Letters Special Issue on the EVLA.
8 pages, 4 figure
- …