论文标题

Specht理想的最小自由分辨率的基本结构的形状$(N-D,D)$

Elementary construction of the minimal free resolution of the Specht ideal of shape $(n-d,d)$

论文作者

Shibata, Kosuke, Yanagawa, Kohji

论文摘要

令$ k $为$ {\ rm char}(k)= 0 $的字段。对于{\ mathbb n} $中的分区$λ$,让$ i^{\ rm sp}_λ$是$ r = k [x_1,\ ldots,x_n] $的理想的理想。这些理想是从几个观点(以及以几个名称)进行了研究的。使用表示理论的高级工具,Berkesch Zamaere等人[BGS]。构建了$ i^{\ rm sp} _ {(n-d,d)} $的最小免费分辨率。本文构建了差形图,还提供了[BGS]结果的基本证明。

Let $K$ be a field with ${\rm char}(K)=0$. For a partition $λ$ of $n \in {\mathbb N}$, let $I^{\rm Sp}_λ$ be the ideal of $R=K[x_1,\ldots,x_n]$ generated by all Specht polynomials of shape $λ$. These ideals have been studied from several points of view (and under several names). Using advanced tools of the representation theory, Berkesch Zamaere et al [BGS]. constructed a minimal free resolution of $I^{\rm Sp}_{(n-d,d)}$ except differential maps. The present paper constructs the differential maps, and also gives an elementary proof of the result of [BGS].

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源