Abstract
We prove that the Grothendieck rings of category CQ(t) over quantum affine algebras Uq′(g(t))(t= 1 , 2) associated with each Dynkin quiver Q of finite type A2n-1 (resp. Dn+1) are isomorphic to one of the categories CQ over the Langlands dual Uq′(Lg(2)) of Uq′(g(2)) associated with any twisted adapted class [Q] of A2n-1 (resp. Dn+1). This results provide simplicity-preserving correspondences on Langlands duality for finite-dimensional representation of quantum affine algebras, suggested by Frenkel–Hernandez.
Original language | English |
---|---|
Pages (from-to) | 401-435 |
Number of pages | 35 |
Journal | Journal of Algebraic Combinatorics |
Volume | 49 |
Issue number | 4 |
DOIs | |
State | Published - 15 Jun 2019 |
Bibliographical note
Funding Information:M. Kashiwara: The research was supported by Grant-in-Aid for Scientific Research (B) 15H03608, Japan Society for the Promotion of Science. S. Oh: This work was supported by NRF Grant # 2016R1C1B2013135.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Combinatorial Auslander–Reiten quivers
- Langlands duality
- Longest element
- Schur–Weyl diagram
- r-Cluster point