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arXiv · 1502.06714

Monoidal categorification of cluster algebras II

Seok-Jin Kang·Masaki Kashiwara·Myungho Kim·Se-jin Oh
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Abstract

We prove that the quantum unipotent coordinate algebra $A_q(\mathfrak{n}(w))\ $ associated with a symmetric Kac-Moody algebra and its Weyl group element $w$ has a monoidal categorification as a quantum cluster algebra. As an application of our earlier work, we achieve it by showing the existence of a quantum monoidal seed of $A_q(\mathfrak{n}(w))$ which admits the first-step mutations in all the directions. As a consequence, we solve the conjecture that any cluster monomial is a member of the upper global basis up to a power of $q^{1/2}$.

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Seok-Jin Kang, Masaki Kashiwara, Myungho Kim, Se-jin Oh. 2015-02-24. Monoidal categorification of cluster algebras II. https://arxiv.org/abs/1502.06714

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