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Laura Colmenarejo, University of Massachusetts- Amherst, An insertion algorithm on multiset partitions with applications to diagram algebras
January 11, 2021 | 12:00 pm - 1:00 pm EST
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.