Cluster algebra structures on module categories over quantum affine algebras

Masaki Kashiwara, Myungho Kim, Se jin Oh, Euiyong Park

Research output: Contribution to journalArticlepeer-review

Abstract

We study monoidal categorifications of certain monoidal subcategories (Formula presented.) of finite-dimensional modules over quantum affine algebras, whose cluster algebra structures on their Grothendieck rings (Formula presented.) are closely related to the category of finite-dimensional modules over quiver Hecke algebra of type (Formula presented.) via the generalized quantum Schur–Weyl duality functors. In particular, when the quantum affine algebra is of type (Formula presented.) or (Formula presented.), the subcategory coincides with the monoidal category (Formula presented.) introduced by Hernandez–Leclerc. As a consequence, the modules corresponding to cluster monomials are real simple modules over quantum affine algebras.

Original languageEnglish
Pages (from-to)301-372
Number of pages72
JournalProceedings of the London Mathematical Society
Volume124
Issue number3
DOIs
StatePublished - Mar 2022

Bibliographical note

Funding Information:
The second, third, and fourth authors gratefully acknowledge for the hospitality of RIMS (Kyoto University) during their visits in 2018 and 2019. The authors would like to thank the anonymous referee for valuable comments and suggestions. The research of M. Kashiwara was supported by Grant‐in‐Aid for Scientific Research (B) 20H01795, Japan Society for the Promotion of Science. The research of M. Kim was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIP)(NRF‐2017R1C1B2007824 and NRF‐2020R1A5A1016126). The research of S.‐j. Oh was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF‐2019R1A2C4069647). The research of E. Park was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIP)(NRF‐2017R1A1A1A05001058 and NRF‐2020R1A5A1016126).

Funding Information:
The second, third, and fourth authors gratefully acknowledge for the hospitality of RIMS (Kyoto University) during their visits in 2018 and 2019. The authors would like to thank the anonymous referee for valuable comments and suggestions. The research of M. Kashiwara was supported by Grant-in-Aid for Scientific Research (B) 20H01795, Japan Society for the Promotion of Science. The research of M. Kim was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIP)(NRF-2017R1C1B2007824 and NRF-2020R1A5A1016126). The research of S.-j. Oh was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2019R1A2C4069647). The research of E. Park was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIP)(NRF-2017R1A1A1A05001058 and NRF-2020R1A5A1016126).

Publisher Copyright:
© 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

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