MASTERS EXAM TALK
"Some Aspects of Groups Acting on Finite Posets"

JiYoon Jung
University of Kentucky

Tuesday, April 15, 2008
9:30 am, 205 Classroom Building

Abstract:

Let P be a finite poset (partially ordered set) and G a subgroup of the full group of automorphisms of P. The action of G on P defines linear representations of G. We present a representation and two examples in detail. In the symmetric group S_n acting on the Boolean algebra B_n, the multiplicity of the irreducible representation lambda in the virtual representation beta_S is equal to the number of standard Young tableaux of shape lambda and descent set S. In the case of the symmetric group S_n acting on the lattice of partitions of an n-set, we find an analogous description of beta_S.