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 …

We present a novel realization of the Z 2× Z 2-graded Lie superalgebra gl (m 1, m 2| n 1, n 2)
inside an algebraic extension of the enveloping algebra of the Z 2-graded Lie superalgebra …

An orthogonal basis of weight vectors for a class of infinite-dimensional representations of
the orthosymplectic Lie superalgebra $\mathfrak {o}\mathfrak {s}\mathfrak {p}(2m+ 1| 2n) $ is …

We give explicit actions of Drinfeld generators on Gelfand–Tsetlin bases of super Yangian
modules associated with skew Young diagrams. In particular, we give another proof that …

We construct explicit formulae for the eigenvalues of certain invariants of the Lie
superalgebra gl (m| n) using characteristic identities. We discuss how such eigenvalues are …

Covariant tensor representations of gl (m| n) occur as irreducible components of tensor
powers of the natural (m+ n)-dimensional representation. We construct a basis of each …

Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl
(m| n), we use characteristic identities to derive explicit matrix element formulae for all gl (m …

We present an overview of characteristic identities for Lie algebras and superalgebras. We
outline methods that employ these characteristic identities to deduce matrix elements of …

For a set of m parafermion operators and n paraboson operators, there are two nontrivial
ways to unify them in a larger algebraic structure. One of these corresponds to the …

In this note, we formulate and prove a branching rule for simple polynomial modules of the
Lie superalgebra. Our branching rules depend on the conjugacy class of a Borel …