Grassmannian上初等交换p-群和丛的表示
Representations of elementary abelian p-groups and bundles on Grassmannians
摘要：
通过对由$r$幂零元生成的群代数$k[t_1,..., t_r]/(t^p_1,..., t_r^p)$的截断多项式子代数的限制，我们开始了初等交换$p$ -群的表示的研究。我们引入了新的几何不变量的基础上的模块的行为限制这样的子代数。我们还引入了常根模和柱脚型模，推广了常Jordan型模，并给出了具有这些性质的模的几种一般构造。我们表明，模块的常根和socle型导致家庭的代数向量丛的格拉斯曼和说明我们的理论与众多的例子。
英文摘要：
We initiate the study of representations of elementary abelian $p$-groups via restrictions to truncated polynomial subalgebras of the group algebra generated by $r$ nilpotent elements, $k[t_1,..., t_r]/(t^p_1,..., t_r^p)$. We introduce new geometric invariants based on the behavior of modules upon restrictions to such subalgebras. We also introduce modules of constant radical and socle type generalizing modules of constant Jordan type and provide several general constructions of modules with these properties. We show that modules of constant radical and socle type lead to families of algebraic vector bundles on Grassmannians and illustrate our theory with numerous examples.
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