MIT-Harvard-MSR Combinatorics Seminar: A Type B analog of the Whitehouse representations


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April 22, 2022 3:30 pm - 4:30 pm
Science Center 232

Sarah Brauner - University of Minnesota

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,  which is based on the preprint