Speaker:  Sarah Brauner, University of Minnesota
Title: On orbit configuration spaces and a Type B analog of the Whitehouse representation
Time: 2:30 PM, Monday, October 18, 2021
Place:  Malott 206

Abstract: The Eulerian idempotents of the symmetric group and the representations they generate, called the Eulerian representations, are a topic of long-standing interest to representation theorists, combinatorialists and topologists. In this talk, I will focus on a property of the Eulerian representations first studied by Whitehouse: that although the Eulerian representations are defined as $S_n$ representations, they can also be understood via a "hidden" action of $S_{n+1}$. More surprisingly still, many of the connections between the Eulerian representations and configuration spaces, equivariant cohomology, and Solomon's descent algebra can be "lifted" to this family of $S_{n+1}$ representations, which we will call the Whitehouse representations. I will then discuss recent work generalizing the above scenario to the hyperoctahedral group, $B_n$. In this setting, configuration spaces will be replaced by certain orbit configuration spaces and Solomon's descent algebra is replaced by the Type B Mantaci-Reutenauer algebra. All of the above will be defined in the talk.


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