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We first compute the denominator formulas for quantum affine algebras of all exceptional types. Then we prove the isomorphisms among Grothendieck rings of categories $${C_Q^{(t)} (t=1,2,3), \mathscr{C}_{\mathscr{Q}}^{(1)}}$$CQ(t)(t=1,2,3),CQ(1) and $${\mathscr{C}_{\mathfrak{Q}}^{(1)}}$$CQ(1). These… Click to show full 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 $${C_Q^{(t)} (t=1,2,3), \mathscr{C}_{\mathscr{Q}}^{(1)}}$$CQ(t)(t=1,2,3),CQ(1) and $${\mathscr{C}_{\mathfrak{Q}}^{(1)}}$$CQ(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.
Journal Title: Communications in Mathematical Physics
Year Published: 2019
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