S. Whitehouse's lifts of the Eulerian representations of S n to S n+1 are reinterpreted, topologically and ring-theoretically, building on the first author's work on A. Ocneanu's theory of permutohedral blades.
Bibliographical noteFunding Information:
First, second authors supported by NSF grants DMS-1148634, DMS-1601961. The paper was written while the first author was an RTG postdoc at the University of Minnesota. The first author is grateful to his doctoral advisor, Adrian Ocneanu, for many interesting discussions related to his work on plates and blades. He also thanks William Norledge for interesting discussions. The second author gratefully acknowledges the hospitality of the American Institute of Mathematics workshop on Representation Stability in June 2016. In particular, he thanks the members of a working group there that included Kevin Casto, Weiyan Chen, Patricia Hersh, Claudiu Raicu, Rita Jimenez-Rolland, Simon Rubinstein-Salzedo, Amin Saied, and David Speyer, for their helpful comments, suggestions, and references. Both authors thank Fran?ois Bergeron, Sarah Brauner, Darij Grinberg, Nick Proudfoot, and Sheila Sundaram for helpful comments, and they thank an anonymous referee for suggestions that improved the exposition.
First, second authors supported by NSF grants DMS-1148634, DMS-1601961. The paper was written while the first author was an RTG postdoc at the University of Minnesota.