Reflection decompositions in the classical Weyl groups

AbstractIn this paper, we present formulas for the number of decompositions of elements of the Weyl groups of type An, Dn and Bn 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 Bédard 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 %plane1D;50A;n are related to the reflection decompositions in Dn