We define a new class of diagram algebras MP_λ(n) indexed by integer partitions λ. When λ is a partition of k, MP_λ(n) is isomorphic to a subalgebra of the partition algebra P_k(n) defined by Jones and Martin. When λ = (1^k), MP_λ(n) is isomorphic to P_k(n). A basis of MP_λ(n) is given in terms of certain bipartite multigraphs. We exhibit a new Schur-Weyl duality between the actions of MP_λ(n) and the symmetric group S_n on the symmetric power Sym^λ(C^n). This is joint work with Sridhar Narayanan and Shraddha Srivastava.
Monday, June 17, 2019
Will need to be edited into an 8 minute video to be presented at a conference. Video should be edited and uploaded by 18th June 2019
The multiset partition algebra