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Mosc. Math. J., 2015, Volume 15, Number 1, Pages 49–72 (Mi mmj548)  

This article is cited in 5 scientific papers (total in 5 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.

DOI: https://doi.org/10.17323/1609-4514-2015-15-1-49-72

Full text: http://www.mathjournals.org/.../2015-015-001-003.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 17B10, 17B70, 05E10, 05E05
Received: April 29, 2014; in revised form November 14, 2014
Language:

Citation: Ghislain Fourier, “New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules”, Mosc. Math. J., 15:1 (2015), 49–72

Citation in format AMSBIB
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\by Ghislain~Fourier
\paper New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 1
\pages 49--72
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\crossref{https://doi.org/10.17323/1609-4514-2015-15-1-49-72}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427411}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. Biswal, G. Fourier, “Minuscule Schubert varieties: poset polytopes, PBW-degenerated Demazure modules, and Kogan faces”, Algebr. Represent. Theory, 18:6 (2015), 1481–1503  crossref  mathscinet  zmath  isi  elib  scopus
    2. D. Kus, P. Littelmann, “Fusion products and toroidal algebras”, Pacific J. Math., 278:2 (2015), 427–445  crossref  mathscinet  zmath  isi  elib  scopus
    3. G. Fourier, “PBW-degenerated Demazure modules and Schubert varieties for triangular elements”, J. Combin. Theory Ser. A, 139 (2016), 132–152  crossref  mathscinet  zmath  isi  elib  scopus
    4. G. Fourier, “Marked poset polytopes: Minkowski sums, indecomposables, and unimodular equivalence”, J. Pure Appl. Algebra, 220:2 (2016), 606–620  crossref  mathscinet  zmath  isi  elib  scopus
    5. A. Bianchi, E. Wilson, “Bases for local Weyl modules for the hyper and truncated current $\mathfrak{sl}_2$-algebras”, J. Algebra, 506 (2018), 509–539  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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