The induced representations of Brauer algebra and the Clebsch-Gordan coefficients of SO(n)

Induced representations of Brauer algebra $D_{f}(n)$ from $S_{f_{1}}\times S_{f_{2}}$ with $f_{1}+f_{2}=f$ are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients (ORCs) of $S_{f_{1}}\times S_{f_{2}}\uparrow D_{f}(n)$ with $f\leq 4$ up to a normalization factor are derived by using the linear equation method. Weyl tableaus for the corresponding Gel'fand basis of SO(n) are defined. The assimilation method for obtaining CG coefficients of SO(n) in the Gel'fand basis for no modification rule involved couplings from IDCs of Brauer algebra are proposed. Some isoscalar factors of $SO(n)\supset SO(n-1)$ for the resulting irrep $[\lambda_{1},~\lambda_{2},~ \lambda_{3},~\lambda_{4},\dot{0}]$ with $\sum\limits_{i=1}^{4}\lambda_{i}\leq .Comment: 48 pages latex, submitted to Journal of Phys.

From Quantum Universal Enveloping Algebras to Quantum Algebras

The ``local'' structure of a quantum group G_q is currently considered to be an infinite-dimensional object: the corresponding quantum universal enveloping algebra U_q(g), which is a Hopf algebra deformation of the universal enveloping algebra of a n-dimensional Lie algebra g=Lie(G). However, we show how, by starting from the generators of the underlying Lie bialgebra (g,\delta), the analyticity in the deformation parameter(s) allows us to determine in a unique way a set of n ``almost primitive'' basic objects in U_q(g), that could be properly called the ``quantum algebra generators''. So, the analytical prolongation (g_q,\Delta) of the Lie bialgebra (g,\delta) is proposed as the appropriate local structure of G_q. Besides, as in this way (g,\delta) and U_q(g) are shown to be in one-to-one correspondence, the classification of quantum groups is reduced to the classification of Lie bialgebras. The su_q(2) and su_q(3) cases are explicitly elaborated.Comment: 16 pages, 0 figures, LaTeX fil

On the Implementation of the Canonical Quantum Simplicity Constraint

In this paper, we are going to discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional General Relativity and Supergravity developed in our companion papers. Since the canonical quadratic simplicity constraint operators have been shown to be anomalous in any dimension D>2, non-standard methods have to be employed to avoid inconsistencies in the quantum theory. We show that one can choose a subset of quadratic simplicity constraint operators which are non-anomalous among themselves and allow for a natural unitary map of the spin networks in the kernel of these simplicity constraint operators to the SU(2)-based Ashtekar-Lewandowski Hilbert space in D=3. The linear constraint operators on the other hand are non-anomalous by themselves, however their solution space will be shown to differ in D=3 from the expected Ashtekar-Lewandowski Hilbert space. We comment on possible strategies to make a connection to the quadratic theory. Also, we comment on the relation of our proposals to existing work in the spin foam literature and how these works could be used in the canonical theory. We emphasise that many ideas developed in this paper are certainly incomplete and should be considered as suggestions for possible starting points for more satisfactory treatments in the future.Comment: 30 pages, 2 figures. v2: Journal version. Comparison to existing approaches added. Discussion extended. References added. Sign error in equation (2.15) corrected. Minor clarifications and correction

The Drinfeld double gl(n) \oplus t_n

The two isomorphic Borel subalgebras of gl(n), realized on upper and lower triangular matrices, allow us to consider the gl(n) \opus t_n algebra as a self-dual Drinfeld double. Compatibility conditions impose the choice of an orthonormal basis in the Cartan subalgebra and fix the basis of gl(n). A natural Lie bialgebra structure on gl(n) is obtained, that offers a new perspective for its standard quantum deformation.Comment: 8 page

From Food to Offspring Down: Tissue-Specific Discrimination and Turn-Over of Stable Isotopes in Herbivorous Waterbirds and Other Avian Foraging Guilds

Isotopic discrimination and turn-over are fundamental to the application of stable isotope ecology in animals. However, detailed information for specific tissues and species are widely lacking, notably for herbivorous species. We provide details on tissue-specific carbon and nitrogen discrimination and turn-over times from food to blood, feathers, claws, egg tissues and offspring down feathers in four species of herbivorous waterbirds. Source-to-tissue discrimination factors for carbon (δ13C) and nitrogen stable isotope ratios (δ15N) showed little variation across species but varied between tissues. Apparent discrimination factors ranged between −0.5 to 2.5‰ for δ13C and 2.8 to 5.2‰ for δ15N, and were more similar between blood components than between keratinous tissues or egg tissue. Comparing these results with published data from other species we found no effect of foraging guild on discrimination factors for carbon but a significant foraging-guild effect for nitrogen discrimination factors

Constraining the Evolution of Zz Ceti

We report our analysis of the stability of pulsation periods in the DAV star (pulsating hydrogen atmosphere white dwarf) ZZ Ceti, also called R548. On the basis of observations that span 31 years, we conclude that the period 213.13 s observed in ZZ Ceti drifts at a rate dP/dt ≤ (5:5 ± 1:9) x 10-15 s s-1, after correcting for proper motion. Our results are consistent with previous Ṗ values for this mode and an improvement over them because of the larger time base. The characteristic stability timescale implied for the pulsation period is ⎸P / Ṗ ⎸=⎹≥ 1:2 Gyr, comparable to the theoretical cooling timescale for the star. Our current stability limit for the period 213.13 s is only slightly less than the present measurement for another DAV, G117-B15A, for the period 215.2 s, establishing this mode in ZZ Ceti as the second most stable optical clock known, comparable to atomic clocks and more stable than most pulsars. Constraining the cooling rate of ZZ Ceti aids theoretical evolutionary models and white dwarf cosmochronology. The drift rate of this clock is small enough that we can set interesting limits on reflex motion due to planetary companions

Ground-gamma band mixing and odd-even staggering in heavy deformed nuclei

It is proposed that the odd-even staggering (OES) in the $\gamma$- bands of heavy deformed nuclei can be reasonably characterized by a discrete approximation of the fourth derivative of the odd-even energy difference as a function of angular momentum $L$. This quantity exhibits a well developed staggering pattern (zigzagging behavior with alternating signs) in rare earth nuclei and actinides with long $\gamma$- bands ($L\geq 10$). It is shown that the OES can be interpreted reasonably as the result of the interaction of the $\gamma$ band with the ground band in the framework of a Vector Boson Model with SU(3) dynamical symmetry. The model energy expression reproduces successfully the staggering pattern in all considered nuclei up to $L=12-13$. The general behavior of the OES effect in rotational regions is studied in terms of the ground--$\gamma$ band-mixing interaction, showing that strong OES effect occurs in regions with strong ground--$\gamma$ band-mixing interaction. The approach used allows a detailed comparison of the OES in $\gamma$ bands with the other kinds of staggering effects in nuclei and diatomic molecules.Comment: 25 pages, 11 postscript figure