This talk is on the combinatorics of partitions. If s is a positive
integer, then an s-core is a particular type of partition which is
important in representation theory. Given any partition which is not an
s-core, there is a well-defined way to make it into an s-core by
removing certain parts.

Now suppose t is another positive
integer, coprime to s. Then a result of Anderson says that there are
only finitely many partitions which are both s- and t-cores. Another
result of Olsson says that if we start with an s-core and take its
t-core, this is still an s-core.

We'll look at the question "when
do two s-cores have the same t-core?". This turns out to be closely
related to alcove geometry for Coxeter groups of type A. One result is a
new proof of Olsson's result, and another is the result that of all the
partitions which are both s- and t-cores, there is one which contains
all the others.

# Cores

Speaker:

Matt Fayers (QMUL)

Date/Time:

Mon, 25/10/2010 - 17:30

Room:

M103

Seminar series: