Quantum Product and Parabolic Orbits in Homogeneous Spaces

Chaput, Manivel, and Perrin proved in [3] a formula describing the quantum product by Schubert classes associated to cominuscule weights in a rational projective homogeneous space X. In the case where X has Picard rank one, we relate this formula to the stratification of X by P-orbits, where P is the parabolic subgroup associated to the cominuscule weight. We deduce a decomposition of the Hasse diagram of X, i.e., the diagram describing the cup-product with the hyperplane class. For all classical Grassmannians, we give a complete description of parabolic orbits associated to cominuscule weights, and we make the decomposition of the Hasse diagram explicit

Quantum product and parabolic orbits in homogeneous spaces

Chaput, Manivel and Perrin proved a formula describing the quantum product by Schubert classes associated to cominuscule weights in a rational projective homogeneous space X. In the case where X has Picard rank one, we link this formula to the stratification of X by P-orbits, where P is the parabolic subgroup associated to the cominuscule weight. We deduce a decomposition of the Hasse diagram of X, i.e the diagram describing the cup-product with the hyperplane class.Comment: 19 pages, 3 figure

On highly regular strongly regular graphs

In this paper we unify several existing regularity conditions for graphs, including strong regularity, $k$-isoregularity, and the $t$-vertex condition. We develop an algebraic composition/decomposition theory of regularity conditions. Using our theoretical results we show that a family of non rank 3 graphs known to satisfy the $7$-vertex condition fulfills an even stronger condition, $(3,7)$-regularity (the notion is defined in the text). Derived from this family we obtain a new infinite family of non rank $3$ strongly regular graphs satisfying the $6$-vertex condition. This strengthens and generalizes previous results by Reichard.Comment: 29 page

Sharemarket performance and the New Zealand dollar : inside the relationships : a thesis presented in partial fulfilment of the requirements for the degree of a Master of Applied Economics, Massey University, Palmerston North, New Zealand

New Zealand is often described as a small open economy with substantial foreign ownership of its assets. The economy is therefore sensitive to exchange rate movements and the sharemarket being the barometer of economic activities should be no exception. Further, exchange rates may also be endogenous to sharemarket fluctuations. This thesis analyses the relationship between the value of the New Zealand dollar vis a vis the currencies of its five largest trading partners and the New Zealand sharemarket performance between 1999 and mid-2005 using the vector autoregression (VAR) and vector error correction model (VECM) approaches. Findings from the research suggest the New Zealand sharemarket is robust to currency fluctuations in both the short- and long- term. The only exception to this is the New Zealand dollar-Australian dollar exchange rate (NZD/AUD), which has a negative short term effect on the sharemarket. The NZD/AUD is also the only exchange rate to depreciate following a positive shock to the sharemarket

Portfolio decisions on life annuities and financial assets with longevity and income uncertainty

There are two stylised facts, namely weak demand for life-annuities and flat age-wealth profile that contradict the life-cycle hypothesis. In this paper we design a theoretical framework, which combines plausible arguments, which have been put forward in the literature to reconcile theory with empirical evidence. Besides the existence of an annuity market and of a public pension system we assume risk-averse individuals who are uncertain about lifetime and disposable income and who have preferences for leaving bequests. It is shown that this framework can contribute to explain the observed portfolio decision in favour of financial assets relatively to annuities.savings; life annuities; bequests; uncertain lifetime; uncertain income; social security