Eulerian representations for real reflection groups

@article{Brauner2022EulerianRF,
  title={Eulerian representations for real reflection groups},
  author={Sarah Brauner},
  journal={Journal of the London Mathematical Society},
  year={2022},
  volume={105}
}
  • Sarah Brauner
  • Published 12 May 2020
  • Mathematics
  • Journal of the London Mathematical Society
The Eulerian idempotents, first introduced for the symmetric group and later extended to all reflection groups, generate a family of representations called the Eulerian representations that decompose the regular representation. In Type A$A$ , the Eulerian representations have many elegant but mysterious connections to rings naturally associated with the braid arrangement. Here, we unify these results and show that they hold for any reflection group of coincidental type — that is, Sn$S_{n}$ , Bn… 
A Type B analog of the Whitehouse representation
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

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