Parastatistics Algebra and Super Semistandard Young Tableaux

TL;DR

This paper explores the algebraic structure of parastatistics involving parabosonic and parafermionic operators, establishing a bijection with super semistandard Young tableaux and introducing a super plactic monoid via algebra deformation.

Contribution

It introduces a novel connection between parastatistics algebra and super semistandard Young tableaux, including a super plactic monoid structure.

Findings

States in the Fock space correspond to SSYT

Deformation yields a super plactic monoid

Provides algebraic insights into parastatistics

Abstract

We consider the parastatistics algebra with both parabosonic and parafermionic operators and show that the states in the universal parastatistics Fock space are in bijection with the Super Semistandard Young Tableaux (SSYT). Using deformation of the parastatistics algebra we get a monoid structure on SSYT which is a super version of the plactic monoid.