PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Ping Xu, Mathieu Stienon, Nigel Higson.

Title:Symmetry and Geometric Structure for the Worpitzky identity
Seminar:GAP Seminar
Speaker:Nick Early, Penn State University
Abstract:
The classical Worpitzky identity for the symmetric group $S_n$ decomposes a cubical lattice into $n!$ simplices of different sizes, each with a multiplicity counted by the number of permutations of $n$ with a fixed number of descents. It is well-known in combinatorics that the Eulerian numbers can be represented as volumes of suitably normalized hypersimplices. We show how the Worpitzky identity encodes localization data for a system of simplicial polyhedral cones which emerge from the $A_n$ simple root system, and becomes now an isomorphism between two new graded, simplicial symmetric group representations.

Room Reservation Information

Room Number:MB106
Date:01 / 27 / 2015
Time:02:30pm - 03:30pm