12,335 research outputs found
Demazure Characters and Affine Fusion Rules
The Demazure character formula is applied to the Verlinde formula for affine
fusion rules. We follow Littelmann's derivation of a generalized
Littlewood-Richardson rule from Demazure characters. A combinatorial rule for
affine fusions does not result, however. Only a modified version of the
Littlewood-Richardson rule is obtained that computes an (old) upper bound on
the fusion coefficients of affine algebras. We argue that this is because
the characters of simple Lie algebras appear in this treatment, instead of the
corresponding affine characters. The Bruhat order on the affine Weyl group must
be implicated in any combinatorial rule for affine fusions; the Bruhat order on
subgroups of this group (such as the finite Weyl group) does not suffice.Comment: 23 pages, TeX, uses harvma
On Fusion Algebras and Modular Matrices
We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal
field theories, affine Kac-Moody algebras at positive integer level, and
quantum groups at roots of unity. Using properties of the modular matrix ,
we find small sets of primary fields (equivalently, sets of highest weights)
which can be identified with the variables of a polynomial realization of the
fusion algebra at level . We prove that for many choices of rank
and level , the number of these variables is the minimum possible, and we
conjecture that it is in fact minimal for most and . We also find new,
systematic sources of zeros in the modular matrix . In addition, we obtain a
formula relating the entries of at fixed points, to entries of at
smaller ranks and levels. Finally, we identify the number fields generated over
the rationals by the entries of , and by the fusion (Verlinde) eigenvalues.Comment: 28 pages, plain Te
On Robin boundary conditions and the Morse potential in quantum mechanics
The physical origin is investigated of Robin boundary conditions for wave
functions at an infinite reflecting wall. We consider both Schr\"odinger and
phase-space quantum mechanics (a.k.a. deformation quantization), for this
simple example of a contact interaction. A non-relativistic particle moving
freely on the half-line is treated as moving on the full line in the presence
of an infinite potential wall, realized as a limit of a Morse potential. We
show that the wave functions for the Morse states can become those for a free
particle on the half-line with Robin boundary conditions. However, Dirichlet
boundary conditions (standard walls) are obtained unless a mass-dependent fine
tuning (to a reflection resonance) is imposed. This phenomenon was already
observed for piece-wise flat potentials, so it is not removed by smoothing. We
argue that it explains why standard quantum walls are standard. Next we
consider the Wigner functions (the symbols of both diagonal and off-diagonal
density operator elements) of phase-space quantum mechanics. Taking the
(fine-tuned) limit, we show that our Wigner functions do reduce to the expected
ones on the half-line. This confirms that the Wigner transform should indeed be
unmodified for this contact interaction.Comment: 19 page
An imaging and spectroscopic study of the planetary nebulae in NGC 5128 (Centaurus A): Planetary nebulae catalogues
Imaging and spectroscopic observations of planetary nebulae (PNe) in the
nearest large elliptical galaxy NGC 5128 (Centaurus A), were obtained to find
more PNe and measure their radial velocities. NTT imaging was obtained in 15
fields in NGC 5128 over an area of about 1 square degree with EMMI using [O
III] and off-band filters. Newly detected sources, combined with literature
PNe, were used as input for VLT FLAMES multi-fibre spectroscopy in MEDUSA mode.
Spectra of the 4600-5100A region were analysed and velocities measured based on
emission lines of [O III]4959,5007A and often H-beta. The chief results are
catalogues of 1118 PN candidates and 1267 spectroscopically confirmed PNe in
NGC 5128. The catalogue of PN candidates contains 1060 PNe discovered with EMMI
imaging and 58 from literature surveys. The spectroscopic PN catalogue has
FLAMES radial velocity and emission line measurements for 1135 PNe, of which
486 are new. Another 132 PN radial velocities are available from the
literature. For 629 PNe observed with FLAMES, H-beta was measured in addition
to [O III]. Nine targets show double-lined or more complex profiles, and their
possible origin is discussed. FLAMES spectra of 48 globular clusters were also
targetted: 11 had emission lines detected (two with multiple components), but
only 3 are PNe likely to belong to the host globular. The total of 1267
confirmed PNe in NGC 5128 with radial velocity measurements (1135 with small
velocity errors) is the largest collection of individual kinematic probes in an
early-type galaxy. This PN dataset, as well as the catalogue of PN candidates,
are valuable resources for detailed investigation of the stellar population of
NGC 5128. [Abridged]Comment: 19 pages, 11 figures. Accepted for publication in Astronomy and
Astrophysics. Tables 7 - 11 available in electronic form at CDS. Replaced
with a few typos fixe
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