Abstract
Let ∆ ⊂ E be a crystallographic root system, and let Q be the root lattice of ∆. Most of this chapter will be devoted to producing certain formal identities in the group ring of Q. The main result of this chapter will be an identity in the polynomial ring ℤ[t] that provides a nontrivial relation between length in W = W(∆) and height in ∆. Such an identity is of interest in its own right. However, the main motivation for such a formula is invariant theory. Its importance in invariant theory will be demonstrated in §27–2, when it is used to calculate the degrees of Weyl groups. The results of this chapter were first proved in MacDonald [2].
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© 2001 Springer Science+Business Media New York
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Kane, R., Borwein, J., Borwein, P. (2001). Formal identities. 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_14
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DOI: https://doi.org/10.1007/978-1-4757-3542-0_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3194-8
Online ISBN: 978-1-4757-3542-0
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