Braid Group Action On The Module Category Of Quantum Affine Algebras

Masaki Kashiwara, Myungho Kim, Se Jin Oh, Euiyong Park

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let g0 be a simple Lie algebra of type ADE and let U'q(g) be the corresponding untwisted quantum affine algebra. We show that there exists an action of the braid group B(g0) on the quantum Grothendieck ring Kt(g) of Hernandez-Leclerc’s category (Formula Presented). Focused on the case of type AN-1, we construct a family of monoidal autofunctors (Formula Presented) on a localization TN of the category of finite-dimensional graded modules over the quiver Hecke algebra of type A. Under an isomorphism between the Grothendieck ring K(TN) of TN and the quantum Grothendieck ring (Formula Presented), the functors (Formula Presented) recover the action of the braid group B(AN-1). We investigate further properties of these functors.

Original languageEnglish
Pages (from-to)13-18
Number of pages6
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume97
Issue number3
DOIs
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021 The Japan Academy

Keywords

  • Quantum affine algebra
  • R-matrix.
  • braid group action
  • quantum Grothendieck ring
  • quiver Hecke algebra

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