Parastatistics Algebra, Young Tableaux and the Super Plactic Monoid

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.

Presented at the International Workshop "Differential Geometry, Noncommutative Geometry, Homology and Fundamental Interactions" in honour of Michel Dubois-Violette, Orsay, April 8-10, 2008

References in corpus (2)

• Tensor fields of mixed Young symmetry type and N-complexes
• Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras

Cited by in corpus (3)

• A class of infinite-dimensional representations of the Lie superalgebra osp(2m+1|2n) and the parastatistics Fock space
• Super jeu de taquin and combinatorics of super tableaux of type A
• A super Littlewood--Richardson type rule