A new Young diagrammatic method for Kronecker products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on the representation theory of Brauer algebras. A general procedure for the decomposition of the tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules, together with trace contractions from a Brauer algebra and some modification rules given by King

Fermi resonance-algebraic model for molecular vibrational spectra

A Fermi resonance-algebraic model is proposed for molecular vibrations, where a U(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into account. The model for a bent molecule XY_2 and a molecule XY_3 is successfully applied to fit the recently observed vibrational spectrum of the water molecule and arsine (AsH_3), respectively, and results are compared with those of other models. Calculations show that algebraic approaches can be used as an effective method for describing molecular vibrations with small standard deviations

Associations between reproduction and work in workers of the Asian hive bee Apis cerana

a b s t r a c t If a honey bee (Apis spp.) colony becomes queenless, about 1/3 of young workers activate their ovaries and produce haploid male-producing eggs. In doing so queenless workers maximize their inclusive fitness because the normal option of vicarious production of relatives via their queen's eggs is no longer available. But if many workers are engaged in reproduction, how does a queenless colony continue to feed its brood and forage? Here we show that in the Asian hive bee Apis cerana hypopharyngeal gland (HPG) size is larger in queenless workers than in queenright workers and that bees undertaking brood-rearing tasks have larger HPG than same-aged bees that are foraging. In queenless colonies, workers with a smaller number of ovarioles are more likely to have activated ovaries. This reinforces the puzzling observation that a large number of ovarioles reduces reproductive success in queenless A. cerana. It further suggests that reproductive workers either avoid foraging or transition to foraging later in life than nonreproductive workers. Finally, our study also showed that ovary activation and larger-than-average numbers of ovarioles had no statistically detectable influence on foraging specialization for pollen or nectar

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.

A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.Comment: Latex, 11 pages, no figure