University of Sydney Algebra Seminar

John Enyang (University of Sydney)

Friday 2 December, 12:05-12:55pm, Carslaw 375

A seminormal form for partition algebras

Partition algebras were defined by Jones and Martin in the 1990s in connection with the Potts model and higher-dimensional statistical mechanics. Jones showed that the partition algebras are in Schur-Weyl duality with the group algebra of the symmetric group \(S_n\) acting on the \(k\)-fold tensor power of its \(n\)-dimensional permutation representation \(V\) . In this talk we will introduce a new presentation of the partition algebras and show how this presentation can be used to obtain explicit combinatorial formulae for the seminormal representations of the partition algebras. Our results generalise to the partition algebras the classical formulae given by Young for the symmetric group.