The Dade Bases And Transfer Ideal Of Invariant Ring F[V]^D_2pof Dihedral Group D_2p In The Modular Case

A basic tool for constructing systems of parameters for rings of invariants of finite groups is Dade bases.Namely,the top Chern classes of the orbits of the Dade bases are a system of parameters for rings of invariants.When the field is infinite,the dual representation of group action admits a Dade bases.In this paper,we mainly describe the construction and the number of Dade bases of dual representation*of dihedral group D2p in the modular case.The next,we restrict our attention to the material structure of the transfer ideal of dihedral group in modular case.The transfer ideal is a nontrivial proper ideal of the invari-ant ring F[V]G in modular case.We can use the height of the transfer ideal in the invariant ring to measure the difference between the transfer ideal and the invariant ring.In the pro-cess of studying the transfer ideal,we determine the invariant subspaces of the elements of order p.Then,the structure of transfer variety under the action of dihedral group D2p is obtained by these invariant subspaces.By using the Hilbert’s Nuiistellensatz method,we obtain the radical ideal of transfer ideal.Finally,we demonstrate the transfer ideal Im(TrG)by the Hironaka decomposition.This paper is composed of three sections.The first chapter gives us a brief introduc-tion of invariant theory of finite groups and the background of the Dade bases and the transfer ideal.In chapter 2,we introduce some basic definitions and theorems.In the last chapter,we obtain the construction and the number of Dade bases of dual representation V*of dihedral group D2p.We compute the height of the transfer ideal.And,the structure of the radical ideal of transfer ideal and the transfer ideal is obtained also.