The quasi-partition algebraAlgebra & Discrete Mathematics
|Zajj Daugherty, Dartmouth College
|Mon, May 20 2013, 12:10PM
Centralizer algebras and algebras that arise via studying endomorphisms of tensor spaces that commute with other familiar groups or algebras (like the general linear group). The commutator relationship provides amazing tools for transferring representation theoretic information back and forth, and can reveal beautiful combinatorial structure. The well-studied partition algebra arises as a centralizer algebra for the symmetric group acting on the k-fold tensor product of its permutation representation. However, the permutation representation is not generally irreducible. In this talk, I will define a new related algebra, the quasi-partition algebra, which also arises as a centralizer algebra for the symmetric group, but now acting on the k-fold tensor product of the large irreducible submodule of the permutation representation. I will give a diagrammatic description and some wonderful combinatorial results. This work is joint with Rosa Orellana.
special day: Monday in addition to Weds this week!