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arXiv · 1802.09253

Categorical relations between Langlands dual quantum affine algebras: Exceptional cases

Se-jin Oh·Travis Scrimshaw
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Abstract

We first compute the denominator formulas for quantum affine algebras of all exceptional types. Then we prove the isomorphisms among Grothendieck rings of categories $C_Q^{(t)}$ $(t=1,2,3)$, $\mathscr{C}_{\mathscr{Q}}^{(1)}$ and $\mathscr{C}_{\mathfrak{Q}}^{(1)}$. These results give Dorey's rule for all exceptional affine types, prove the conjectures of Kashiwara-Kang-Kim and Kashiwara-Oh, and provides the partial answers of Frenkel-Hernandez on Langlands duality for finite dimensional representations of quantum affine algebras of exceptional types.

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BibTeXRIS

Se-jin Oh, Travis Scrimshaw. 2018-02-26. Categorical relations between Langlands dual quantum affine algebras: Exceptional cases. https://doi.org/10.1007/s00220-019-03287-w

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