Monoidal categorification of cluster algebras II
Monoidal categorification of cluster algebras II
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发表时间：
2015-02
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通讯作者：
Seok-Jin Kang;M. Kashiwara;Myungho Kim;Se-jin Oh
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作者：
Seok-Jin Kang;M. Kashiwara;Myungho Kim;Se-jin Oh
证明了与对称Kac-Moody代数及其Weyl群元w相关联的量子幂幺坐标代数Aq（n（w））有一个么半群范畴，即量子簇代数.作为我们早期工作的应用，我们通过证明$A_q（\mathfrak{n}（w））$的量子幺半群种子的存在性来实现它，该种子允许所有方向上的第一步突变。因此，我们解决了猜想，任何集群单项式是一个成员的上整体基础的一个权力的q^{1/2}$。
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 $q^{1/2}$.