Irfan Habib
Any maximal root subsystem of a finite crystallographic reduced root system is either a closed root subsystem or its dual is a closed root subsystem in the dual root system. In this article, we classify the maximal root subsystems of an…
$\pi$-systems are fundamental in the study of Kac-Moody Lie algebras since they arise naturally in the embedding problems. Dynkin introduced them first and showed how they also appear in the classification of semisimple subalgebras of a…
Motivated by a construction of Gorelik and Shaviv, we show that the real roots of a root generated subalgebra associated with a $\pi$-system contained in the positive roots are obtained by successive applications of even and odd reflections…
We prove an inductive formula to construct a path from the highest weight element to any given vertex in the crystal graph of the polytope realization of the Kirillov-Reshetikhin crystal $KR^{i,m}$ of type $A$. For $i \leq 2$ or $i \geq…
Radchenko and Villegas characterized the chordal graphs by the inverse of their independence polynomials being Horn hypergeometric series in Radchenko et al. in 2021. In this paper, we reprove their result using some elementary…
The derived algebra of a symmetrizible Kac-Moody algebra $\lie g$ is generated (as a Lie algebra) by its root spaces corresponding to real roots. In this paper, we address the natural reverse question: given any subset of real root vectors,…
Any symmetric closed subset of a finite crystallographic root system must be a closed subroot system. This is not, in general, true for real affine root systems. In this paper, we determine when this is true and also give a very explicit…
Grid computing has made substantial advances during the last decade. Grid middleware such as Globus has contributed greatly in making this possible. There are, however, significant barriers to the adoption of Grid computing in other fields,…
We outline the approach being developed in the neuGRID project to use provenance management techniques for the purposes of capturing and preserving the provenance data that emerges in the specification and execution of workflows in…
We outline the approach being developed in the neuGRID project to use provenance management techniques for the purposes of capturing and preserving the provenance data that emerges in the specification and execution of workflows in…
By abstracting Grid middleware specific considerations from clinical research applications, re-usable services should be developed that will provide generic functionality aimed specifically at medical applications. In the scope of the…
Grid Computing has made substantial advances in the past decade; these are primarily due to the adoption of standardized Grid middleware. However Grid computing has not yet become pervasive because of some barriers that we believe have been…