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arXiv · 1403.4758

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

Ghislain Fourier
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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.

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Ghislain Fourier. 2014-03-19. New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules. https://arxiv.org/abs/1403.4758

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