Nordic Topology Meeting 
Friday, August 28, 10:00 - 10:45

Greg Arone: A branching rule for the Lie representation and partition complexes.

The Hilton-Milnor theorem gives a decomposition of the topological free group generated by a wedge sum of connected spaces. There is an analogous algebraic decomposition of the free Lie algebra generated by a direct sum of free abelian groups. I will begin by showing how the algebraic Hilton-Milnor theorem gives rise to a kind of “branching rule” for the Lie representation. More precisely, one gets a decomposition for the restriction of the Lie representation to a Young subgroup. I will then show how one can “geometrically realize” this to obtain an analogous decomposition of the partition complex.