Abstract
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.
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Serre, JP. (2018). On the mod p reduction of orthogonal representations. In: Kac, V., Popov, V. (eds) Lie Groups, Geometry, and Representation Theory. Progress in Mathematics, vol 326. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02191-7_18
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DOI: https://doi.org/10.1007/978-3-030-02191-7_18
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-02190-0
Online ISBN: 978-3-030-02191-7
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