Ghislain Fourier
Published 2014-03-19Version 1
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.
Gröbner basis for fusion products
Filtration of tensor product of local Weyl modules for $\mathfrak{sl}_{n+1}[t]$
Defining relations of fusion products and Schur positivity
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