## 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

Funding Information:Received 21 October 2017; revised 3 April 2018; published online 19 June 2018. 2010 Mathematics Subject Classification 81R50, 16G99, 16T25,17B37 (primary). The research of Kashiwara was supported by Grant-in-Aid for Scientific Research (B) 15H03608, Japan Society for the Promotion of Science. The research of Kim was supported by the National Research Foundation of Korea(NRF) Grant funded by the Korea government(MSIP) (NRF-2017R1C1B2007824). The research of Oh was supported by the National Research Foundation of Korea(NRF) Grant funded by the Korea government(MSIP) (NRF-2016R1C1B2013135).

Publisher Copyright:

© 2018 London Mathematical Society

## Keywords

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