arXiv subjects

Irfan Habib

Publications and source records attributed to Irfan Habib.

12 recordsLinked to original sources

arXiv2025

Graded embeddings, root generated subalgebras and $π$-systems for quasisimple Kac-Moody superalgebras

Motivated by a construction of Gorelik and Shaviv, we show that the real roots of a root generated subalgebra associated with a $π$-system contained in the positive roots are obtained by successive applications of even and odd reflections to the $π$-system, and that they form a real closed subroot system. Using this result, we establish an analogue of Dynkins bijection in the setting of symmetrizable quasisimple Kac-Moody superalgebras. In addition, we obtain several results on root strings in the super setting, analogous to those of Billig and Pianzola, and show that graded embeddings arise as root generated subalgebras associated with linearly independent $π$-systems.

math.RA↗

arXiv2025

On the Polytope Model and Near End node Isomorphisms of Type $A$ Kirillov--Reshetikhin Crystals

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 $i \geq n-1$, we provide explicit formulas of the same by only using the lowering crystal operators and in those cases, using these paths, we determine the explicit image of any element under the affine crystal isomorphisms between the polytope and the tableau realizations of the Kirillov-Reshetikhin crystals.

math.CO↗

arXiv2024

Maximal root subsystems of affine reflection systems and duality

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 affine reflection system (reduced and non-reduced) and prove that this result holds in much more generality for reduced affine reflection systems. Moreover, we explicitly determine when a maximal root subsystem is a maximal closed root subsystem. Using our classification, at the end, we characterize the maximal root systems of affine reflection systems with nullity less than or equal to $2$ using Hermite normal forms; especially for Saito's EARS of nullity $2.$ This in turn classifies the maximal subgroups of the Weyl group of an affine reflection system that are generated by reflections.

math.RA↗

arXiv2024

On the characterization of chordal graphs using Horn hypergeometric series

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 combinatorial methods. Our proof is different from their proof, and it is based on the connection between the inverse of the multi-variate independence polynomials and the multi-colored chromatic polynomials of graphs, established by Arunkumar et al. in 2018.

math.CO↗

arXiv2024

$π$-systems and the embedding problem for rank $2$ Kac-Moody Lie algebras

$π$-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 semisimple Lie algebra. In this article, we explicitly classify the $π$-systems associated to rank $2$ Kac-Moody Lie algebras and prove that in most of the cases they are linearly independent. This classification allows us to determine the root generated subalgebras and which in turn determines all possible Kac-Moody algebras that can be embedded in a rank $2$ Kac-Moody algebra as subalgebras generated by real root vectors. Additionally, following the work of Naito we provide examples illustrating how Borcherds Kac-Moody algebras can also be embedded inside a rank $2$ Kac-Moody algebra.

math.RA↗

arXiv2023

Root generated subalgebras of symmetrizable Kac-Moody algebras

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, is the Lie subalgebra of $\lie g$ generated by these again the derived algebra of a Kac-Moody algebra? We call such Lie subalgebras root generated, give an affirmative answer to the above question and show that there is a one-to-one correspondence between them, real closed subroot systems and $π$-systems contained in the positive system of $\lie g$. Finally, we apply these identifications to all untwised affine types in order to classify symmetric regular subalgebras first introduced by Dynkin in the finite-dimensional setting. We show that any root generated subalgebra associated to a maximal real closed subroot system can be embedded into a unique maximal symmetric regular subalgebra.

math.RA↗

arXiv2022

On symmetric closed subsets of real affine root systems

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 description of symmetric closed subsets of real affine root systems. At the end, using our results, we study the correspondence between symmetric closed subsets of real affine root systems and the regular subalgebras generated by them.

math.RA↗

arXiv2014

Research Traceability using Provenance Services for Biomedical Analysis

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 biomedical analyses. In the neuGRID project a provenance service has been designed and implemented that is intended to capture, store, retrieve and reconstruct the workflow information needed to facilitate users in conducting user analyses. We describe the architecture of the neuGRID provenance service and discuss how the CRISTAL system from CERN is being adapted to address the requirements of the project and then consider how a generalised approach for provenance management could emerge for more generic application to the (Health)Grid community.

cs.DB↗

arXiv2012

Reusable Services from the neuGRID Project for Grid-Based Health Applications

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 neuGRID project, generic services are being designed and developed which will be applied to satisfy the requirements of neuroscientists. These services will bring together sources of data and computing elements into a single view as far as applications are concerned, making it possible to cope with centralised, distributed or hybrid data and provide native support for common medical file formats. Services will include querying, provenance, portal, anonymization and pipeline services together with a 'glueing' service for connection to Grid services. Thus lower-level services will hide the peculiarities of any specific Grid technology from upper layers, provide application independence and will enable the selection of 'fit-for-purpose' infrastructures. This paper outlines the design strategy being followed in neuGRID using the glueing and pipeline services as examples.

cs.SE↗

arXiv2012

Research Traceability using Provenance Services for Biomedical Analysis

cs.DB↗

arXiv2007

PhantomOS: A Next Generation Grid Operating System

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 caused by the adoption of middleware centric approaches. These barriers include: scant support for major types of applications such as interactive applications; lack of flexible, autonomic and scalable Grid architectures; lack of plug-and-play Grid computing and, most importantly, no straightforward way to setup and administer Grids. PhantomOS is a project which aims to address many of these barriers. Its goal is the creation of a user friendly pervasive Grid computing platform that facilitates the rapid deployment and easy maintenance of Grids whilst providing support for major types of applications on Grids of almost any topology. In this paper we present the detailed system architecture and an overview of its implementation.

cs.DC↗

arXiv2006

From Grid Middleware to a Grid Operating System

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, most notably day-to-day user computing environments. We will demonstrate in this paper that this is primarily due to the limitations of the existing Grid middleware which does not take into account the needs of everyday scientific and business users. In this paper we will formally advocate a Grid Operating System and propose an architecture to migrate Grid computing into a Grid operating system which we believe would help remove most of the technical barriers to the adoption of Grid computing and make it relevant to the day-to-day user. We believe this proposed transition to a Grid operating system will drive more pervasive Grid computing research and application development and deployment in future.

cs.DC↗