Séminaire Lotharingien de Combinatoire, 86B.12 (2022), 12 pp.

Sarah Brauner

A Type B Analog of the Whitehouse Representation

Abstract. We give a Type B analog of Whitehouse's lifts of the Eulerian representations from Sn to Sn+1 by introducing a family of Bn-representations that lift to Bn+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 Z2-orbit configuration space of R3. We show that the lifted Bn+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.

Received: November 25, 2021. Accepted: March 4, 2022. Final version: April 1, 2022.

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