Monoidal categories of modules over quantum affine algebras of type A and B

Masaki Kashiwara, Myungho Kim, Se jin Oh

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We construct an exact tensor functor from the category A of finite-dimensional graded modules over the quiver Hecke algebra of type A∞ to the category CBn(1) of finite-dimensional integrable modules over the quantum affine algebra of type Bn 1. It factors through the category T2n, which is a localization of A. As a result, this functor induces a ring isomorphism from the Grothendieck ring of T2n (ignoring the gradings) to the Grothendieck ring of a subcategory C0 Bn(1) of CBn(1). Moreover, it induces a bijection between the classes of simple objects. Because the category T2n is related to categories (Formula presented.) (t = 1, 2) of the quantum affine algebras of type A(1) 2n-1, we obtain an interesting connection between those categories of modules over quantum affine algebras of type A and type B. Namely, for each t = 1, 2, there exists an isomorphism between the Grothendieck ring of C0 Bn(1) and the Grothendieck ring of (Formula presented.), which induces a bijection between the classes of simple modules.

Original languageEnglish
Pages (from-to)43-77
Number of pages35
JournalProceedings of the London Mathematical Society
Volume118
Issue number1
DOIs
StatePublished - Jan 2019

Keywords

  • 16G99
  • 16T25,17B37 (primary)
  • 81R50

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