A seminormal form 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.

Published version. 51 pages, includes figures and tables

References in corpus (3)

• On blocks of Deligne's category Rep(S_t)
• Jucys-Murphy elements and a presentation for partition algebras
• Partition Algebra, its Characterization and Representations

Cited by in corpus (6)

• Jucys-Murphy elements and a presentation for partition algebras
• The Center of the Partition Algebra
• The block structure of the partition algebras in characteristic $p\ge 0$
• A new approach to the representation theory of the partition category
• Skew cell modules for diagram algebras
• Quantum walled Brauer algebra: commuting families, Baxterization, and representations