This article is cited in 11 papers

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

Ghislain Fourier<sup>ab

a</sup> 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.

MSC: 17B10, 17B70, 05E10, 05E05

Received: April 29, 2014; in revised form November 14, 2014

Language: English

DOI: 10.17323/1609-4514-2015-15-1-49-72

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