论文标题
过滤普通和拉格朗日格拉曼尼亚人
Filtering cohomology of ordinary and Lagrangian Grassmannians
论文作者
论文摘要
本文研究了一个积极的整数$ m $，这是由学位元素最多按$ m $ $ $ $ $ $ $ $ $ M $产生的复杂Grassmanians的同类圈。我们以两种方式建立了由于雷纳和延伸导致的sublgebra的希尔伯特系列的猜想。第一个根据$ k $ - 缀合的操作重新诠释了它，这暗示了subgebras的两个猜想基础，这意味着他们的猜想。第二个引入了与拉格朗日格拉曼尼亚人的共同学的类似猜想。
This paper studies, for a positive integer $m$, the subalgebra of the cohomology ring of the complex Grassmannians generated by the elements of degree at most $m$. We build in two ways upon a conjecture for the Hilbert series of this subalgebra due to Reiner and Tudose. The first reinterprets it in terms of the operation of $k$-conjugation, suggesting two conjectural bases for the subalgebras that would imply their conjecture. The second introduces an analogous conjecture for the cohomology of Lagrangian Grassmannians.
