Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Faculty Publications Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Creator An entity primarily responsible for making the resource Pal, Souvik Title A name given to the resource Quasi-finite modules over affine and extended affine Lie algebras Date A point or period of time associated with an event in the lifecycle of the resource 01-01-2025 Source A related resource from which the described resource is derived Mathematische Zeitschrift;Volume;311;Issue;3;Article No.;63; Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1007/s00209-025-03854-z" target="_blank" rel="noreferrer noopener">https://doi.org/10.1007/s00209-025-03854-z</a> <br /><br /><a href="https://www.scopus.com/pages/publications/105016754081?origin=resultslist" target="_blank" rel="noreferrer noopener">https://www.scopus.com/pages/publications/105016754081?origin=resultslist</a> Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Pal S., Department of Mathematics, Indian Institute of Science, CV Raman Road, Karnataka, Bengaluru, 560012, India, Department of Sciences and Humanities, CHRIST University, Mysore Road, Bangalore, 560 074, India Description An account of the resource In this paper, we consider irreducible quasi-finite (or equivalently weakly integrable) modules, with non-trivial action of the core, over the extended affine Lie algebras (EALAs) whose centerless cores are multiloop algebras. The centerless cores of all but one family of EALAs having nullity greater than 1 are known to admit such multiloop realizations. For any such (untwisted) EALA, we show that the irreducible quasi-finite modules are either integrable with the center of the underlying core acting trivially, or restricted generalized highest weight (GHW) modules. We further prove that in the nullity 2 case, these irreducible restricted GHW modules turn out to be highest weight type modules, thereby classifying the irreducible quasi-finite modules over all such EALAs. In particular, we obtain the classification of irreducible quasi-finite modules over toroidal Lie algebras, minimal EALAs and toroidal EALAs of nullity 2. Along the way, we also completely classify the irreducible weakly integrable modules over affine Kac-Moody algebras (RaoFutorny in Trans. Am. Math. Soc. 361(10): 54355455, 2009). Our results generalize the well-known work of Chari (Invent. Math. 85(2):317335, 1986) and ChariPressley (Math. Ann. 275(1):87104, 1986) concerning the classification of irreducible integrable modules over (nullity 1) affine KacMoody algebras. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025. Subject The topic of the resource Extended affine Lie algebras; Fgc condition; Highest weight type modules; Quasi-finite modules; Weakly integrable modules Publisher An entity responsible for making the resource available Springer Science and Business Media Deutschland GmbH Relation A related resource ISSN: 255874; Language A language of the resource English Type The nature or genre of the resource Article Rights Information about rights held in and over the resource Restricted Access; Hardcopy may be available in the library Format The file format, physical medium, or dimensions of the resource online