论文标题
三维模块化表示不变的环
Rings of invariants for three dimensional modular representations
论文作者
论文摘要
令$ p> 3 $为质量数。我们计算小学Abelian $ p $ -group $（\ Mathbb z/p \ Mathbb z）^r $的不变性的戒指，价格为$ 3 $二维通用表示。此外，我们证明这些不变的环是与嵌入尺寸$ \ lceil r/2 \ rceil +3 $的完整交点环。 这证明了[CSW]中坎贝尔，Shank和Wehlau的猜想，他们以$ r = 3 $的形式证明了这一点，后来，皮尔伦和Shank以$ r = 4 $证明了这一点。
Let $p>3$ be a prime number. We compute the rings of invariants of the elementary abelian $p$-group $(\mathbb Z/p\mathbb Z)^r$ for $3$-dimensional generic representations. Furthermore we show that these rings of invariants are complete intersections rings with embedding dimension $\lceil r/2\rceil +3$. This proves a conjecture of Campbell, Shank and Wehlau in [CSW], which they proved for $r=3$, and later Pierron and Shank proved it for $r=4$.
