摘要翻译:
考虑一个不是Grassmaninan的部分标志品种$x$。也考虑它的上同调环${\rm H}^*(X,\zz)$被赋予由Schubert变体的Poincar对偶类形成的基。E.Richmond在引用{Richmond:recursion}中指出,对于较小的标志变种,${\rm H}^*(X,\zz)$中乘积的某些系数结构是两个这样的系数的乘积。现在考虑一个没有定向循环的箭袋。如果$\alpha$和$\beta$表示两个维度向量,则$\alpha\circ\beta$表示一般$\alpha+\beta$维度表示的$\alpha$维度子表示的数目。在\cite{dw:comb}中,H.Derksen和J.Weyman将一些数字$\alpha\circ\beta$表示为两个较小的此类数字的乘积。本文的目的是用同样的方法证明上述两个结果的两个推广。
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英文标题:
《Multiplicative formulas in Cohomology of $G/P$ and in quiver
representations》
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作者:
Nicolas Ressayre (I3M)
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
Consider a partial flag variety $X$ which is not a grassmaninan. Consider also its cohomology ring ${\rm H}^*(X,\ZZ)$ endowed with the base formed by the Poincar\'e dual classes of the Schubert varieties. In \cite{Richmond:recursion}, E. Richmond showed that some coefficient structure of the product in ${\rm H}^*(X,\ZZ)$ are products of two such coefficients for smaller flag varieties. Consider now a quiver without oriented cycle. If $\alpha$ and $\beta$ denote two dimension-vectors, $\alpha\circ\beta$ denotes the number of $\alpha$-dimensional subrepresentations of a general $\alpha+\beta$-dimensional representation. In \cite{DW:comb}, H. Derksen and J. Weyman expressed some numbers $\alpha\circ\beta$ as products of two smaller such numbers. The aim of this work is to prove two generalisations of the two above results by the same way.
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PDF链接:
https://arxiv.org/pdf/0812.2122