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This article is cited in 10 scientific papers (total in 10 papers)
New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules
Ghislain Fourierab a Mathematisches Institut, Universität zu Köln, Germany
b School of Mathematics and Statistics, University of Glasgow, UK
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.
Key words and phrases:
PBW filtration, fusion product, Pieri rule, Schur positivity.
Received: April 29, 2014; in revised form November 14, 2014
Citation:
Ghislain Fourier, “New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules”, Mosc. Math. J., 15:1 (2015), 49–72
Linking options:
https://www.mathnet.ru/eng/mmj548 https://www.mathnet.ru/eng/mmj/v15/i1/p49
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