Positive Energy Unitary Irreducible Representations of the Superalgebra osp(1|8,R)

We continue the study of positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R). We present the full list of these UIRs. We give the Proof of the case osp(1|8,R).Comment: 17 pages, v2: changed format to include figur

Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary

In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Sklyanin’s derivation in the periodic case. Once we have the generating function, we obtain the corresponding Gaudin Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the generic form of the Bethe vectors such that the off-shell action of the generating function becomes exceedingly compact and simple. In this way—by obtaining Bethe equations and the spectrum of the generating function—we fully implement the algebraic Bethe ansatz for the generalized trigonometric Gaudin model.info:eu-repo/semantics/publishedVersio

Public pension expenditure in the EPC and the European Commission projections: an analysis of the projection results

This paper reviews the projections of the Economic Policy Committee and the European Commission on age-related expenditure carried out in 2005. It takes a closer look at the results of public pension expenditure projections with a view of analysing the timing of projected changes and the driving factors behind pension expenditure increases, as well as the sensitivity of the projections to certain economic and demographic assumptions. It intends to provide a more in-depth understanding on the evolution of projected public pension expenditure and thereby contributing to the debate on the assessment of the long-term sustainability of public finances.The paper serves as a quality assessment of public pension expenditure projections, which were carried out by the experts in each Member State. It takes a careful look at the differences in results across Member States. It concludes that differences in the results can qualitatively be explained by different pension policies and systems as well as different population and labour force projections and economic assumptions. However, the contribution of different factors to the results or whether the differences in the results are fully explicable by these factors cannot be disentangled.Pension expenditure, pension projections, ageing, dependency ratio, pension take-up ratio, benefit ratio, Salom�ki

Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain, of arbitrary spin-$s$, in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.Comment: 39 pages. Typos corrected. arXiv admin note: substantial text overlap with arXiv:1405.7398, arXiv:1412.139