Mathematics Colloquia and Seminars

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The Eulerian idempotents of the symmetric group generate a family of representations—the Eulerian representations—that have connections to configuration spaces, equivariant cohomology, and Solomon's descent algebra. These representations are defined in terms of S_n, but can be “lifted” to representations of S_{n+1} called the Whitehouse representations. I will describe this story in detail and present recent work generalizing it to the hyperoctahedral group (e.g. Type B). In this setting, configuration spaces will be replaced by certain orbit configuration spaces and Solomon's descent algebra is replaced by the Mantaci-Reutenauer algebra. All of the above will be defined in the talk.