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.
Matt Fayers (QMUL)
Mon, 25/10/2010 - 17:30