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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

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.