An explicit isomorphism between quantum and classical sl(n)

Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum group associated to g is isomorphic as an algebra to the trivial deformation of the universal enveloping algebra of g. In this paper we construct explicitly such an isomorphism when g = sl(n), previously known only for n=2.Comment: 32 pages. Slightly modified introduction. To appear in Transformation Group

Poles of finite-dimensional representations of Yangians

Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over $\mathbb{C}$, and let $Y_{\hbar}(\mathfrak{g})$ be the Yangian of $\mathfrak{g}$. In this paper, we initiate the study of the set of poles of the rational currents defining the action of $Y_{\hbar}(\mathfrak{g})$ on an arbitrary finite-dimensional vector space $V$. We prove that this set is completely determined by the eigenvalues of the commuting Cartan currents of $Y_{\hbar}(\mathfrak{g})$, and therefore encodes the singularities of the components of the $q$-character of $V$. We obtain sufficient conditions for a tensor product of finite-dimensional irreducible representations to be cyclic and irreducible, in terms of these sets of poles. Furthermore, we show that these sets are precisely the zeros of the Yangian analogue of the Baxter polynomials defined by Frenkel and Hernandez. For an irreducible representation, we obtain a concrete description of its sets of poles, in terms of the zeroes of the underlying Drinfeld polynomials and the inverse of the $q$-Cartan matrix of $\mathfrak{g}$. In particular, our results yield a complete classification of the finite-dimensional irreducible representations of the Yangian double.Comment: 61 pages. Significantly revised version. Updates include: modified introduction; relation with Baxter polynomials; proof of the Conjecture (for simply-laced types) from the previous version, valid for any type; relation with denominator formulae; and more references to the literatur

The R-matrix of the affine Yangian

Let g be an affine Lie algebra with associated Yangian Y_hg. We prove the existence of two meromorphic R-matrices associated to any pair of representations of Y_hg in the category O. They are related by a unitary constraint and constructed as products of the form R(s)=R^+(s)R^0(s)R^-(s), where R^+(s) = R^-_{21}(-s)^{-1}. The factor R^0(s) is a meromorphic, abelian R-matrix, with a WKB-type singularity in h, and R^-(s) is a rational twist. Our proof relies on two novel ingredients. The first is an irregular, abelian, additive difference equation whose difference operator is given in terms of the q-Cartan matrix of g. The regularization of this difference equation gives rise to R^0(s) as the exponentials of the two canonical fundamental solutions. The second key ingredient is a higher order analogue of the adjoint action of the affine Cartan subalgebra of g on Y_hg. This action has no classical counterpart, and produces a system of linear equations from which R^-(s) is recovered as the unique solution. Moreover, we show that both operators give rise to the same rational R-matrix on the tensor product of any two highest-weight representations.Comment: 57 pages. 5 figure

Bioaccumulation of heavy metals in Spinacea oleracea grown in distillery effluent irrigated soil

The aim of the present study was to estimate the accumulation of heavy metals in Spinacea oleracea plant grown in Distillery Effluent (DE) irrigated soil. The results revealed that there was an increase in the metal contents Fe (+2.39%), Zn (+14.27%), Ni (+70.45%), Cd (+34.15%)and Cr (+20.46%) of soil irrigated with DE. In case of S. oleracea grown in the DE irrigated soil, it was observed that there was maximum concentration of Fe (353.24±7.94 mg/kg) and Zn (78.95±7.59 mg/kg) in leaves and that of Cr (54.19±8.39 mg/kg), Cd (7.73±1.41 mg/kg) and Ni (66.47±3.65 mg/kg) in root. The value of Bio-concentration factor (BCF) was found maximum for Cr (2.00) in comparison to other metals in the S. oleracea irrigated with DE. The value of Transfer factor (TF) was found maximum for Zn (TF- 1.51) for the soil irrigated with DE in comparison to soil irrigated with Bore well water (BWW). The DE can be a source of contamination to the soil as some toxic metals may also be transferred to roots and then to leaves in S. oleracea. The practice of continuous irrigation of agricultural land by DE may increase the risk of metal contamination in growing food crops to cause human health risks

A Comparative Analysis of Micro Finances: An Economic Impact of Micro Finance upon Income Level of People in Kavrepalanchok District, Nepal

Master thesis Business Administration - University of Agder 2016Micro Finance, one of the essential banking services providing institution has a major contribution upon the economic development of people and nation. It targets mostly to low income generating people and assist them to enhance their life style in a better way. It provides financial services to such people and tries to eradicate the poverty from the nation. Kavrepalanchok district in Nepal, with an area of 1,396 square kilometer with the population of more than 450,000 is a gateway to capital city Kathmandu. The people in this district rely upon business and agricultural income. Micro Finance has significant effect upon the level of income in this district. The distance from the main city Kathmandu has also adverse effect upon the level of income and economic development of the people in Kavrepalanchok district. It assists to uplift the level of income of the people here by providing small loan with lower interest rate. It provides loan in a group of people. Micro Finance in this region generally provides its financial services only to women from a single family. Further, Micro Finances with different established dates and locations have their individual economic impact upon their clients. This comparative economic impacts result to their level of financial performance. Keywords: Agriculture, Business, Economic Development, Income Level, Micro Financ