报告题目：Modular matrix invariants under some transpose actions

报 告 人：任珊

主 持 人：陈锋

时 间：2026 年 11 月 12 日 13 点

地 点：正心楼 1314

主办单位：数学与统计学院

报告人简介： 任珊，博士毕业于东北师范大学基础数学专业，研究方向为表示论、代数不变量理论及李理论。在 Finite Field Appl., Comm. Algebra, Kyushu J. Math., J. Algebra Appl.等国际数学期刊上发表 sci 论文 7 篇。

观点综述：Consider the special linear group of degree 2 over an arbitrary finite field, acting on the full space of 2 × 2-matrices by transpose.We explicitly construct a generating set for the corresponding modular matrix invariant ring, demonstrating that this ring is a hypersurface.Using a recent result on a-invariants of Cohen-Macaulay algebras, we determine the Hilbert series of this invariant ring, and our method avoids seeking the generating relation. Additionally, we prove that the modularmatrix invariant ring of the group of upper triangular 2 × 2-matricesis also a hypersurface. This is a joint work with Yin Chen.