TY - JOUR

T1 - Categorical Relations Between Langlands Dual Quantum Affine Algebras

T2 - Exceptional Cases

AU - Oh, Se jin

AU - Scrimshaw, Travis

N1 - Funding Information:
Se-jin Oh was partially supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIP) (NRF-2016R1C1B2013135). Travis Scrimshaw was partially supported by the Australian Research Council DP170102648.
Funding Information:
The authors would like to thank Masaki Kashiwara for useful discussions. The authors would like to thank the anonymous referee for useful comments. T.S. would like to thank Ewha Womans University for its hospitality during his stay in June, 2017, where this work began. S.O. would like to thank The University of Queensland for its hospitality during his stay in February, 2018. This work benefited from computations using SageMath [65,66].
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85062587695&partnerID=8YFLogxK

U2 - 10.1007/s00220-019-03287-w

DO - 10.1007/s00220-019-03287-w

M3 - Article

AN - SCOPUS:85062587695

SN - 0010-3616

VL - 368

SP - 295

EP - 367

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -