Categorical Relations Between Langlands Dual Quantum Affine Algebras: Exceptional Cases

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 ) , C Q ( 1 ) and C Q ( 1 ) . These results give Dorey’s rule for all exceptional affine types, prove the co...

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Bibliographic Details
Published in:Communications in mathematical physics 2019-05, Vol.368 (1), p.295-367
Main Authors: Oh, Se-jin, Scrimshaw, Travis
Format: Article
Language:English
Subjects:
Algebra
Classical and Quantum Gravitation
Complex Systems
Isomorphism
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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 ) , C Q ( 1 ) and C 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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03287-w