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MIT Combinatorics Seminar

Blocks of multipartitions

Matthew Fayers  (MIT)

Wednesday, April 04, 2007       3:15 pm (!!!)    Room 2-146 (!!!)


ABSTRACT

Let λ be a Young diagram, and e a positive integer. Given a node (i,j) of λ, we define its residue to be j-i (mod e), and we define the content of λ to be the multiset consisting of the residues of all its nodes. Now we say that two partitions lie in the same e-block if their Young diagrams have the same content. These notions all come from the modular representation theory of the symmetric group, where (if e is a prime) the partitions in an e-block are the labels of the Specht modules lying in an e-block of Sn. It is pretty well known that two partitions lie in the same e-block if and only if they have the same e-weight and e-core, and this makes e-blocks much easier to understand from a combinatorial point of view.

The same set-up applies to multipartitions, and has representation-theoretic importance. But the appropriate notions of weight and core for multipartitions are not so easy to come by. In this talk I'll explain my attempts to define and study these.