Filtration of tensor product of local Weyl modules for \mathfraksl_n+1[t]

2024/05/20 by Divya Setia, Setia, Divya, Shushma Rani +3
Mathematics · #17B10 #17B35 #17B65 #17B67 #17B70 #Advanced Algebra and Geometry #FOS: Mathematics #Graph theory and applications #Representation Theory (math.RT) #Rings and Algebras (math.RA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2405.11944

openalex publication_date 2024/05/20 · openalex created_date 2024/05/22 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the tensor product of local Weyl modules for \mathfraksl_n+1[t] whose highest weights are multiples of the first and n^th fundamental weights. We determine the graded character of these tensor product modules in terms of the graded character of local Weyl modules and prove that these modules admit a filtration whose successive quotients are either truncated Weyl modules or fusion products of Demazure modules. Furthermore, we establish that the truncated Weyl modules appearing as quotients in the filtration of tensor products of local Weyl modules of \mathfraksl₃[t] are indeed isomorphic to fusion products of irreducible \mathfraksl₃[t]-modules which establish the independence of a family of fusion product modules of \mathfraksl₃[t] from the set of its evaluation parameters.

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