## Abstract

Let Uq′(g) be a twisted affine quantum group of type AN(2) or DN(2) and let g_{0} be the finite-dimensional simple Lie algebra of type A_{N} or D_{N}. For a Dynkin quiver of type g_{0}, we define a full subcategory CQ(2) of the category of finite-dimensional integrable Uq′(g)-modules, a twisted version of the category CQ(1) introduced by Hernandez and Leclerc. Applying the general scheme of affine Schur–Weyl duality, we construct an exact faithful KLR-type duality functor FQ(2):Rep(R)→CQ(2), where Rep (R) is the category of finite-dimensional modules over the quiver Hecke algebra R of type g_{0} with nilpotent actions of the generators x_{k}. We show that FQ(2) sends any simple object to a simple object and induces a ring isomorphism [InlineEquation not available: see fulltext.].

Original language | English |
---|---|

Pages (from-to) | 1987-2015 |

Number of pages | 29 |

Journal | Selecta Mathematica, New Series |

Volume | 22 |

Issue number | 4 |

DOIs | |

State | Published - 1 Oct 2016 |

### Bibliographical note

Publisher Copyright:© 2016, Springer International Publishing.

## Keywords

- Quantum affine algebra
- Quantum group
- Quiver Hecke algebra