Monoidal categorification and quantum affine algebras

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}^{\p...

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Published inCompositio mathematica Vol. 156; no. 5; pp. 1039 - 1077
Main Authors Kashiwara, Masaki, Kim, Myungho, Oh, Se-jin, Park, Euiyong
Format Journal Article
LanguageEnglish
Published London Cambridge University Press 01.05.2020
Subjects
Algebra
Invariants
Modules
Mutation
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ISSN0010-437X
1570-5846
DOI10.1112/S0010437X20007137

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Summary: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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ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X20007137