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Partition Algebras
Algebra & Discrete Mathematics| Speaker: | Tom Halverson, Macalester College |
| Location: | 2112 MSB |
| Start time: | Fri, Apr 25 2008, 1:10PM |
Description
The partition algebra is the centralizer of the symmetric group on
tensor powers of its permutation representation. It has beautiful
combinatorial representation theory: its dimension is the number of
set partitions, its irreducible representations are labeled by
integer partitions, a basis of the irreducible representations is
given by vacillating tableaux, and there is a Schensted algorithm
that relates these objects. Recently, in joint work with Arun Ram and
Nat Thiem, we have defined a q-analog of the partition algebra, which
is the centralizer of the finite general linear group GLn(Fq ) on a
different kind of tensor space. I will show some preliminary results
on this algebra and, in particular, give a nice q-dimension identity
which the Schensted insertion picks up.