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arXiv · 1705.07542

Categorical relations between Langlands dual quantum affine algebras: Doubly laced types

Masaki Kashiwara·Se-jin Oh
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Abstract

We prove that the Grothendieck rings of category $\mathcal{C}^{(t)}_Q$ over quantum affine algebras $U_q'(\g^{(t)})$ $(t=1,2)$ associated to each Dynkin quiver $Q$ of finite type $A_{2n-1}$ (resp. $D_{n+1}$) is isomorphic to one of category $\mathcal{C}_{\mQ}$ over the Langlands dual $U_q'({^L}\g^{(2)})$ of $U_q'(\g^{(2)})$ associated to any twisted adapted class $[\mQ]$ of $A_{2n-1}$ (resp. $D_{n+1}$). This results provide partial answers of conjectures of Frenkel-Hernandez on Langlands duality for finite-dimensional representation of quantum affine algebras.

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BibTeXRIS

Masaki Kashiwara, Se-jin Oh. 2017-05-22. Categorical relations between Langlands dual quantum affine algebras: Doubly laced types. https://arxiv.org/abs/1705.07542

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