Monoidal categorification and quantum affine algebras

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

Published 2019-10-18Version 1

We introduce and investigate new invariants on the pair of modules $M$ and $N$ over quantum affine algebras $U_q'(\mathfrak{g})$ by analyzing their associated R-matrices. From new invariants, we provide a criterion for a monoidal category of finite-dimensional integrable $U_q'(\mathfrak{g})$-modules to become a monoidal categorification of a cluster algebra.