Abstract
In this section, we introduce the concept of the Poincaré series of a graded algebra and illustrate how it can be used to analyze the structure of rings of invariants. The main structural result is Molien’s theorem, which is obtained in § 17–2. The remaining sections are applications of that theorem. In particular, Molien’s theorem is used in § 17–3 to demonstrate how pseudo-reflections arise naturally in invariant theory. This is the first indication of an intrinsic relation between invariant theory and pseudo-reflections. Much of the remainder of this book will be concerned with the invariant theory of pseudo-reflection groups.
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© 2001 Springer Science+Business Media New York
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Kane, R., Borwein, J., Borwein, P. (2001). Poincaré series. 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_18
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DOI: https://doi.org/10.1007/978-1-4757-3542-0_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3194-8
Online ISBN: 978-1-4757-3542-0
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