Linear quivers, generic extensions and Kashiwara operators

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• 作者：Bangming Deng ; Jie Du ; Guanglian Zhang
• 关键词：s ; Weakly pseudoconvex boundaries ; Tangential Cauchy-Riemann cohomology
  MSC ; 32V15 ; 32V05
• 刊名：Indagationes Mathematicae
• 出版年：2007
• 出版时间：2007
• 年：2007
• 卷：18
• 期：1
• 页码：3-21
• 全文大小：715 K

文摘

In the present paper, we introduce the generic extension graph G of a Dynkin or cyclic quiver Q and then compare this graph with the crystal graph C for the quantized enveloping algebra associated to Q via two maps _Q, _Q : Ω → Λ_Q induced by generic extensions and Kashiwara operators, respectively, where Λ_Q is the set of isoclasses of nilpotent representations of Q, and Ω is the set of all words on the alphabet I, the vertex set of Q. We prove that, if Q is a (finite or infinite) linear quiver, then the intersection of the fibres _Q⁻¹ (λ) and KQ⁻¹ (λ) is non-empty for every λ Λ _Q. We will also show that this non-emptyness property fails for cyclic quivers.