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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-02191-7_18
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-02190-0
Online ISBN: 978-3-030-02191-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)