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Reflection decompositions in the classical Weyl groups

✍ Scribed by Alain Goupil

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 523 KB
Volume: 137
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0163-x

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✦ Synopsis

In this paper, we present formulas for the number of decompositions of elements of the Weyl groups of type A., D. and B, as products of a number of reflections that is not necessarily minimal. For this purpose, we consider the poset of conjugacy classes of W introduced in B6dard and Goupil (1992) for the symmetric group. This poset describes the action of the set of reflections of a reflection group on its conjugacy classes. In particular, we show how the reflection decompositions in the symmetric group 65. are related to the reflection decompositions in D..

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