The Poincaré Series of Relative Invariants of Finite Pseudo-reflection Groups in Finite Fields
Qin Xiao-e · Journal of Sichuan Normal University · 2014
Let F q( q = pm,m≥1) be a finite field with characteristic p,V = Fn q be the n-dimensional vector space over F q and G be a finite pseudo-reflection group.Let χ:G→F* q be a 1-dimensional representation of G.In this article we show that χ( σ) =( det σ)α,0≤α≤r-1,where σ∈G,r is the order of σ and r|q-1.In addition,we prove the Molien's Theorem in finite fields,and use the Molien's Theorem of invariants to compute the Poincare series of relative invariants in finite fields.