Parastatistics Algebra, Young Tableaux and the Super Plactic Monoid

Abstract

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.a Michel découvreur de senties inconnus où la beauté mathématique rejoint la simplicité des lois de la physique.

Notes on Schubert, Grothendieck and Key Polynomials

“…Recall that reduced generalized plactic algebra QPC n is the quotient of the generalized plactic algebra by the two-sided ideal J n introduced in Definition 5.18. (A) Super plactic monoid [38,56]. Assume that the set of generators U := {u 1 , .…”

Parafermions, Parabosons and Representations of 𝔰𝔬(∞) and 𝔬𝔰𝔭(1|∞)

“…Thus in the series of papers [12,21] and the present one we have given solutions to a problem that had been open for a long time. An interesting next step would be to investigate the representations of the parastatistics algebra [14] consisting of a combined system of m pairs of parafermions and n pairs of parabosons, known to be related to representations of the orthosymplectic Lie superalgebra osp(2m + 1|2n) [17].…”

Young Tableaux and Homotopy Commutative Algebras

“…A nice combinatorial proof of this fact was given by Chaturvedi [3]. The GL(V )model PS(V ) enjoys the universal property that every parastatistics Fock representation specified by the parastatistics order p ∈ N 0 is a factor of PS(V ) [4], [10]. The differential ∂ commutes with the GL(V ) action and the homology H • (g, K) is also a GL(V )-module.…”