On the mod p reduction of orthogonal representations
We show that the reduction mod p of an orthogonal, or symplectic, linear representation of a group (or of an algebra with involution) is also orthogonal, or symplectic. The proof makes use of a (perhaps new) construction: the lower and upper “middles” of a pair of lattices.
KeywordsBrauer-Nesbitt lattice middle orthogonal semisimplification
Mathematics Subject Classification (2010):20Cxx 13F30
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