On Modular Vector Invariant Fields

• 作者: Ying Han Runxuan Zhang
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 749-752
• 页数: 4页
• 语种: 英文
• DOI: 10.1142/S1005386720000620

摘要

Let Fq be a finite field of any characteristic and GL(n,Fq) be the general linear group over Fq.Suppose W denotes the standard representation of GL(n,Fq),and GL(n,Fq) acts diagonally on the direct sum of W and its dual space W*.Let G be any subgroup of GL(n,Fq).Suppose the invariant field Fq (W)G =Fq (f1,f2,...,fk),where f1,f2,...,fk in Fq[W]G are homogeneous invariant polynomials.We prove that there exist homogeneous polynomials l1,l2,...,ln in the invariant ring Fq[W ⊕ W*]G such that the invariant field Fq(W ⊕ W*)G is generated by {f1,f2,...fk,l1,l2,...,ln} over Fq.