Open Mathematics (May 2022)
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.
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