Math Colloquium: An insertion algorithm on multiset partitions with applications to diagram algebras

Dr. Laura Colmenarejo, Professor of Mathematics, North Carolina State University.

In algebraic combinatorics, the Robinson-Schensted-Knuth algorithm is a fundamental correspondence between words and pairs of semistandard tableaux illustrating identities of dimensions of irreducible representations of several groups. In this talk, I will present a generalization of the Robinson-Schensted-Knuth algorithm to the insertion of two-row arrays of multisets. This generalization leads to new enumerative results that have representation-theoretic interpretation as decomposition of centralizer algebras and the spaces they act on. I will also present a variant of this algorithm for diagram algebras that has the remarkable property that it is well-behaved with respect to restricting a representation to a subalgebra.

Refreshments to follow.