论文标题
负面的卡塔兰数字和简单的calabi-yau类别中的简单系统
Positive Fuss-Catalan numbers and Simple-minded systems in negative Calabi-Yau categories
论文作者
论文摘要
我们在$ d $ -simple的系统（$ d $ -smss）之间建立了$（ - d）$（d）$（$ d $ smsss）$（calabi-yau群集类别$ {\ cal c _ { - d}}}（h）$和$ {\ cal d^{\ rm b}} $ cal cal cal cal的$ {\ cal d^{\ cal d^{ d^{\ ge 1-d} $ for dynkin类型的遗传代数$ h $和$ d \ ge 1 $。我们表明，$ d $ -smss中的$ {\ cal c _ { - d}}（h）$是相应的weyl group $ w $的积极的烦恼 - catalan $ c_ {d}^{+}（w）$，通过应用此研究和buan-reitaten-reiten-reiten-thomas'和formin-read-read-read compery of fomin-nos os os os os os n os fomin-the comperiation。我们的结果基于精制版本的Silting-$ t $结构通信。
We establish a bijection between $d$-simple-minded systems ($d$-SMSs) of $(-d)$-Calabi-Yau cluster category ${\cal C_{-d}}(H)$ and silting objects of ${\cal D^{\rm b}}(H)$ contained in $\cal D^{\le 0}\cap \cal D^{\ge 1-d}$ for hereditary algebra $H$ of Dynkin type and $d\ge 1$. We show that the number of $d$-SMSs in ${\cal C_{-d}}(H)$ is the positive Fuss-Catalan number $C_{d}^{+}(W)$ of the corresponding Weyl group $W$, by applying this bijection and Buan-Reiten-Thomas' and Zhu's results on Fomin-Reading's generalized cluster complexes. Our results are based on a refined version of silting-$t$-structure correspondence.
