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2018 | OriginalPaper | Chapter

Orbit Decompositions of Unipotent Elements in the Generalized Symmetric Spaces of \(\operatorname {SL}_2(\mathbb {F}_{q})\)

Authors : Catherine Buell, Vicky Klima, Jennifer Schaefer, Carmen Wright, Ellen Ziliak

Published in: Advances in the Mathematical Sciences

Publisher: Springer International Publishing

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Abstract

In this chapter, we determine the orbits of the fixed-point group on the unipotent elements in the generalized symmetric space for each involution of \({\mathrm{SL}}_2(\mathbb {F}_q)\) with \({\mathrm{char}}\left (\mathbb {F}_q \right ) \neq 2\). We discuss how the generalized symmetric spaces can be decomposed into semisimple elements and unipotent elements, and why this decomposition allows the orbits of the fixed-point group on the entire generalized symmetric space to be more easily classified. We conclude by providing a description of and a count for the orbits of the fixed-point group on the unipotent elements in the generalized symmetric space for each involution of \({\mathrm{SL}}_2(\mathbb {F}_q)\).

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Metadata
Title
Orbit Decompositions of Unipotent Elements in the Generalized Symmetric Spaces of
Authors
Catherine Buell
Vicky Klima
Jennifer Schaefer
Carmen Wright
Ellen Ziliak
Copyright Year
2018
Book
Advances in the Mathematical Sciences

Print ISBN: 978-3-319-98683-8

Electronic ISBN: 978-3-319-98684-5

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-98684-5_5

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