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

zbMATH Open1383.17006arXiv1403.4758MaRDI QIDQ2801865

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Publication date: 22 April 2016

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Abstract: New graded modules for the current algebra of $mathfrak{sl}_n$ are introduced. Relating these modules to the fusion product of simple $mathfrak{sl}_n$-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 $mathfrak{sl}_n$-modules and use them to provide decomposition formulas for these new modules in important cases.

Full work available at URL: https://arxiv.org/abs/1403.4758

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