Auslander-Reiten quiver of type D and generalized quantum affine Schur-Weyl duality

Se jin Oh

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We first provide an explicit combinatorial description of the Auslander-Reiten quiver ΓQ of finite type D. Then we can investigate the categories of finite dimensional representations over the quantum affine algebra Uq'(Dn+1(i)) (i=1, 2) and the quiver Hecke algebra RDn+1 associated to Dn+1 (n≥3), by using the combinatorial description and the generalized quantum affine Schur-Weyl duality functor. As applications, we can prove that Dorey's rule holds for the category Rep(RDn+1) and prove an interesting difference between multiplicity free positive roots and multiplicity non-free positive roots.

Original languageEnglish
Pages (from-to)203-252
Number of pages50
JournalJournal of Algebra
Volume460
DOIs
StatePublished - 15 Aug 2016

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

  • Auslander-Reiten quiver
  • Generalized quantum affine Schur-Weyl duality
  • Primary
  • Quiver Hecke algebra
  • Secondary

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