Categorical Relations Between Langlands Dual Quantum Affine Algebras: Exceptional Cases

Se jin Oh; Travis Scrimshaw

doi:10.1007/s00220-019-03287-w

Categorical Relations Between Langlands Dual Quantum Affine Algebras: Exceptional Cases

Se jin Oh, Travis Scrimshaw

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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 CQ(t)(t=1,2,3),CQ(1) and 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.

Original language	English
Pages (from-to)	295-367
Number of pages	73
Journal	Communications in Mathematical Physics
Volume	368
Issue number	1
DOIs	https://doi.org/10.1007/s00220-019-03287-w
State	Published - 1 May 2019

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© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

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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 CQ(t)(t=1,2,3),CQ(1) and CQ(1). These results give Dorey{\textquoteright}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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Categorical Relations Between Langlands Dual Quantum Affine Algebras: Exceptional Cases

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