Partition Algebra, its Characterization and Representations

TL;DR

This paper provides a detailed characterization and explicit Young's seminormal form representations for the partition algebra A_3(Q), enhancing understanding of its structure and representations.

Contribution

It introduces new characterizations of A_n(Q) and A_{n-1/2}(Q) along with explicit seminormal form representations for A_3(Q).

Findings

Explicit Young's seminormal form representations for A_3(Q).

New characterizations of A_n(Q) and A_{n-1/2}(Q).

Improved understanding of partition algebra structures.

Abstract

In this note we give representations for the partition algebra A_3(Q) in Young's seminormal form. For this purpose, we also give characterizations of A_n(Q) and$A_{n-1/2}(Q).