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Monoidal categorification and quantum affine algebras

  • Masaki Kashiwara (a1) (a2), Myungho Kim (a3), Se-jin Oh (a4) and Euiyong Park (a5)

Abstract

We introduce and investigate new invariants of pairs of modules $M$ and $N$ over quantum affine algebras $U_{q}^{\prime }(\mathfrak{g})$ by analyzing their associated $R$ -matrices. Using these new invariants, we provide a criterion for a monoidal category of finite-dimensional integrable $U_{q}^{\prime }(\mathfrak{g})$ -modules to become a monoidal categorification of a cluster algebra.

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The research of M. Kashiwara was supported by Grant-in-Aid for Scientific Research (B) 15H03608, 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). 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).

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Keywords

MSC classification

Monoidal categorification and quantum affine algebras

  • Masaki Kashiwara (a1) (a2), Myungho Kim (a3), Se-jin Oh (a4) and Euiyong Park (a5)

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