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

الأصل · EN

New graded modules for the current algebra of slₙ are introduced. Relating these modules to the fusion product of simple slₙ-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 slₙ-modules and use them to provide decomposition formulas for these new modules in important cases.