On configuration spaces and Whitehouse's lifts of the Eulerian representations

TL;DR

This paper explores the topological and algebraic structures of Whitehouse's lifts of Eulerian representations, providing new interpretations and connections to permutohedral blades and ring theory.

Contribution

It offers a novel topological and ring-theoretic reinterpretation of Whitehouse's lifts, extending previous work on permutohedral blades and Eulerian representations.

Findings

Reinterpreted Whitehouse's lifts topologically and ring-theoretically

Connected Eulerian representations to permutohedral blades

Extended the theoretical framework of symmetric group representations

Abstract

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.