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

Summary:

New graded modules for the current algebra of 𝔰𝔩_n are introduced. Relating these modules to the fusion product of simple 𝔰𝔩_n 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 𝔰𝔩_n-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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