Abstract
The most fundamental question we can ask about the invariant theory of a pseudo-reflection group is how to calculate its degrees and exponents. In this chapter, we explain how to characterize exponents in terms of data about the eigenvalues of elements from the group. The relation given in its full generality is due to PianzolaWeiss [1]. Their result is an extension of the fundamental work of Shephard-Todd [1] and Solomon [1].
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kane, R., Borwein, J., Borwein, P. (2001). Eigenvalues for reflection groups. In: Borwein, J., Borwein, P. (eds) Reflection Groups and Invariant Theory. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3542-0_32
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3542-0_32
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3194-8
Online ISBN: 978-1-4757-3542-0
eBook Packages: Springer Book Archive