PBW Theoretic Approach to the Module Category of Quantum Affine Algebras

M. J.A. Masaki Kashiwara, Myungho Kim, Se Jin Oh, Euiyong Park

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let (Formula presented) be a quantum affine algebra of untwisted affine ADE type and let (Formula presented) be Hernandez-Leclerc’s category. For a duality datum D in (Formula presented), we denote by (Formula presented) the quantum affine Weyl-Schur duality functor. We give a sufficient condition for a duality datum D to provide the functor (Formula presented) sending simple modules to simple modules. Moreover, under the same condition, the functor (Formula presented) has compatibility with the new invariants introduced by the authors. Then we introduce the notion of cuspidal modules in (Formula presented), and show that all simple modules in (Formula presented) can be constructed as the heads of ordered tensor products of cuspidal modules. We next state that the ordered tensor products of cuspidal modules have the unitriangularity property.

Original languageEnglish
Pages (from-to)33-37
Number of pages5
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume97
Issue number6
DOIs
StatePublished - 2021

Keywords

  • Cuspidal modules
  • Hernandez-Leclerc category
  • quantum affine Weyl-Schur duality
  • quantum affine algebra
  • quiver Hecke algebra

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