The transfer ideal under the action of orthogonal group in modular case

Abstract

In this paper, we study the structures of the invariant subspaces under the action of orthogonal group O2ν(Fq,S){O}_{2\nu }\left({F}_{q},S). In particular, we give a detailed description of 2-codimensional invariant subspaces. Moreover, we show that the height of transfer ideal Im(TrO2ν(Fq,S)){\rm{Im}}({{\rm{Tr}}}^{{O}_{2\nu }\left({F}_{q},S)}) is 2 and give a primary decomposition for the radical ideal of this transfer ideal.

Keywords

• transfer ideal
• transfer variety
• invariant subspace
• orthogonal group
• 47a15
• 20m12