A seminormal form for partition algebras

TL;DR

This paper introduces a new presentation for partition algebras and derives explicit combinatorial formulas for their seminormal representations, generalizing classical Young formulas for symmetric groups.

Contribution

It provides a novel presentation and explicit formulas for seminormal representations of partition algebras, extending classical symmetric group results.

Findings

Explicit combinatorial formulas for seminormal representations

Generalization of Young's formulas to partition algebras

New presentation for partition algebras

Abstract

Using a new presentation for partition algebras (J. Algebraic Combin. 37(3):401-454, 2013), we derive explicit combinatorial formulae for the seminormal representations of the partition algebras. These results generalise to the partition algebras the classical formulae given by Young for the symmetric group.