Parastatistics Algebra, Young Tableaux and the Super Plactic Monoid

TL;DR

This paper explores the structure of the parastatistics algebra, linking it to super semistandard Young tableaux and introducing a super plactic monoid through algebra deformation.

Contribution

It establishes a correspondence between parastatistics states and SSYT, and introduces a super plactic monoid structure via algebra deformation.

Findings

States correspond to SSYT with constraints

Deformation yields a super plactic monoid

Provides algebraic and combinatorial insights

Abstract

The parastatistics algebra is a superalgebra with (even) parafermi and (odd) parabose creation and annihilation operators. The states in the parastatistics Fock-like space are shown to be in one-to-one correspondence with the Super Semistandard Young Tableaux (SSYT) subject to further constraints. The deformation of the parastatistics algebra gives rise to a monoidal structure on the SSYT which is a super-counterpart of the plactic monoid.