New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules

Fourier, G. (2015) New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules. Moscow Mathematical Journal, 15(1), pp. 49-72.

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Abstract

New graded modules for the current algebra of sln are introduced. Relating these modules to the fusion product of simple sln-modules and local Weyl modules of truncated current algebras shows their expected impact on several outstanding conjectures. We further generalize results on PBW filtrations of simple sln-modules and use them to provide decomposition formulas for these new modules in important cases.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Fourier, Dr Ghislain
Authors: Fourier, G.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Moscow Mathematical Journal
Journal Abbr.:MMJ
Publisher:Independent University of Moscow
ISSN:1609-3321
ISSN (Online):1609-4514
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