## 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 C_{Bn}(1) of finite-dimensional integrable modules over the quantum affine algebra of type B_{n} ^{1}. It factors through the category T_{2n}, which is a localization of A. As a result, this functor induces a ring isomorphism from the Grothendieck ring of T_{2n} (ignoring the gradings) to the Grothendieck ring of a subcategory C^{0} _{Bn}(1) of C_{Bn}(1). Moreover, it induces a bijection between the classes of simple objects. Because the category T_{2n} 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 C^{0} _{Bn}(1) and the Grothendieck ring of (Formula presented.), which induces a bijection between the classes of simple modules.

Original language | English |
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Pages (from-to) | 43-77 |

Number of pages | 35 |

Journal | Proceedings of the London Mathematical Society |

Volume | 118 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2019 |

### Bibliographical note

Publisher Copyright:© 2018 London Mathematical Society

## Keywords

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