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Moscow Mathematical Journal

Volume 15, Issue 1, January–March 2015  pp. 49–72.

New Homogeneous Ideals for Current Algebras: Filtrations, Fusion Products and Pieri Rules

Authors:  Ghislain Fourier
Author institution:Mathematisches Institut, Universitӓt zu Kӧln, Germany, and School of Mathematics and Statistics, University of Glasgow, UK


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.

2010 Math. Subj. Class. Primary: 17B10, 17B70, 05E10, 05E05.

Keywords: PBW filtration, fusion product, Pieri rule, Schur positivity.

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