16,942 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
Lithic economies and community organization at La Laguna, Tlaxcala
Site-wide, assemblage-based lithic analyses help to elucidate community dynamics including variability in domestic economies, technological skill and decision making, exchange networks, and ritual practices. In this study we present the results of an analysis of over 36,000 lithic artifacts from the site of La Laguna, Tlaxcala. We compare Middle to Late Formative period (ca. 600–400 b.c.) and Terminal Formative period (ca. 100 b.c.–a.d. 150) deposits to examine transformations associated with urbanization and state formation during this interval. The residents of La Laguna had relatively equal and ample access to obsidian, and most production was organized independently by households. We identify blade production zones and variability in consumption patterns suggestive of different domestic, communal, and ceremonial activities. The introduction of bloodletters, elaborate large bifacial knives, and zoomorphic eccentrics to the Terminal Formative assemblage may indicate the emergence of higher statuses, new social roles, and militaristic symbolism during this period
IT outsourcing in the public sector local government: experiences of the management and selection of IT service providers
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