A Homotopy Equivalence for Partitions related to
Liftings of $S_{n1}$modules to $S_{n}$
Sheila Sundaram
December 2,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

We give a homotopy equivalence to explain an $S_{n1}$module
isomorphism which occurs frequently in the homology of subposets
of the partition lattice $\Pi_n.$
The isomorphism in question is a necessary, but not sufficient,
condition for the existence
of a lifting to the symmetric group $S_n,$ of the $S_{n1}$module involved.
It has also been observed in certain deformations of the free Lie algebra.
The topological explanation allows us to
generate further examples in subposets of $\Pi_n.$
We show that, in these two contexts, it is
often accompanied by an $S_{n}$action on
the $S_{n1}$module occurring in the isomorphism.
A wellknown example is the Whitehouse lifting of the homology of
$\Pi_{n1}.$

Speaker's Contact Info: sheila(atsign)claude.math.wesleyan.edu
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