A Type B analog of the Whitehouse representation

We give a Type B analog of Whitehouse’s lifts of the Eulerian representations from S_n to S_n+1 by introducing a family of B_n -representations that lift to B_n+1 . As in Type A , we interpret these representations combinatorially via a family of orthogonal idempotents in the Mantaci-Reutenauer algebra, and topologically as the graded pieces of the cohomology of a certain ℤ _2 -orbit configuration space of ℝ ^3 . We show that the lifted B_n+1 -representations also have a configuration space interpretation, and further parallel the Type A story by giving analogs of many of its notable properties, such as connections to equivariant cohomology and the Varchenko-Gelfand ring.