Related papers: The parity operator for parafermions and paraboson…
It is known that the defining triple relations of m pairs of parafermion operators and n pairs of paraboson operators with relative parafermion relations can be considered as defining relations for the Lie superalgebra osp(2m+1|2n) in terms…
The defining relations (triple relations) of n pairs of parafermion operators f_j^\pm (j=1,...,n) are known to coincide with a set of defining relations for the Lie algebra so(2n+1) in terms of 2n generators. With the common Hermiticity…
The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight…
When the relative commutation relations between a set of m parafermions and n parabosons are of ``relative parafermion type'', the underlying algebraic structure is the classical orthosymplectic Lie superalgebra osp(2m+1|2n). The relative…
The algebraic structure generated by the creation and annihilation operators of a system of m parafermions and n parabosons, satisfying the mutual parafermion relations, is known to be the Lie superalgebra osp(2m+1|2n). The Fock spaces of…
An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+1|2n) is introduced. These representations are particular lowest weight representations V(p), with a…
It is known that the defining relations of the orthosymplectic Lie superalgebra osp(1|2n) are equivalent to the defining (triple) relations of n pairs of paraboson operators $b^\pm_i$. In particular, with the usual star conditions, this…
The parastatistics Fock spaces of order $p$ corresponding to an infinite number of parafermions and parabosons with relative paraboson relations are constructed. The Fock spaces are lowest weight representations of the $Z_2 \times…
The Fock-like representations of the Relative Parabose Set (\textsc{Rpbs}) algebra in a single parabosonic and a single parafermionic degree of freedom are investigated. It is shown that there is an infinite family (parametrized by the…
Bosons and Parabosons are described as associative superalgebras, with an infinite number of odd generators. Bosons are shown to be a quotient superalgebra of Parabosons, establishing thus an even algebra epimorphism which is an immediate…
We unify parastatistics, defined as triple operator algebras represented on Fock space, in a simple way using the transition number operators. We express them as a normal ordered expansion of creation and annihilation operators. We discuss…
Generalized quantum statistics, such as paraboson and parafermion statistics, are characterized by triple relations which are related to Lie (super)algebras of type B. The correspondence of the Fock spaces of parabosons, parafermions as…
This paper is about the orbifold theory of parafermion vertex operator algebras $K(osp(1|2),k)$ associated to the affine vertex operator superalgebra $L_{\widehat{osp(1|2)}}(k,0)$ with any positive integer $k$. Among the main results, we…
Starting from the observation that for neighboring orders $p=2^{n}-1, p'=2^{n+1}-1 $ of the well-known Green's representations of parafermi algebra there exists a specifiable interordinal relationship, matrices with similar properties are…
A Fock space is introduced that admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimenisonal…
We consider the algebra $R$ generated by three elements $A,B,H$ subject to three relations $[H,A]=A$, $[H,B]=-B$ and $\{A,B\}=f(H)$. When $f(H)=H$ this coincides with the Lie superalgebra $osp(1/2)$; when $f$ is a polynomial we speak of…
We explore the Fock spaces of the parafermionic algebra introduced by H.S. Green. Each parafermionic Fock space allows for a free minimal resolution by graded modules of the graded 2-step nilpotent subalgebra of the parafermionic creation…
The anomalous bilinear commutation relations satisfied by the components of the Green's ansatz for paraparticles are shown to derive from the comultiplication of the paraboson or parafermion algebra. The same provides a generalization of…
We introduce a class of non-commutative geometries, loosely referred to as para-spaces, which are manifolds equipped with sheaves of non-commutative algebras called para-algebras. A differential analysis on para-spaces is investigated,…
The Lie algebra generated by $m\ $ $p$-dimensional Grassmannian Dirac operators and $m\ $ $p$-dimensional vector variables is identified as the orthogonal Lie algebra $\mathfrak{so}(2m+1)$. In this paper, we study the space $\mathcal{P}$ of…