The-graded Lie superalgebra and new parastatistics representations
NI Stoilova, J Van der Jeugt - Journal of Physics A: Mathematical …, 2018 - iopscience.iop.org
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 …
are of'relative parafermion type', the underlying algebraic structure is the classical …
The Z2× Z2-graded general linear Lie superalgebra
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 …
inside an algebraic extension of the enveloping algebra of the Z 2-graded Lie superalgebra …
A class of infinite-dimensional representations of the Lie superalgebra and the parastatistics Fock space
NI Stoilova, J Van der Jeugt - Journal of Physics A: Mathematical …, 2015 - iopscience.iop.org
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 …
the orthosymplectic Lie superalgebra $\mathfrak {o}\mathfrak {s}\mathfrak {p}(2m+ 1| 2n) $ is …
Gelfand–Tsetlin bases of representations for super Yangian and quantum affine superalgebra
K Lu - Letters in Mathematical Physics, 2021 - Springer
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 …
modules associated with skew Young diagrams. In particular, we give another proof that …
Invariants and reduced matrix elements associated with the Lie superalgebra gl (m| n)
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 …
superalgebra gl (m| n) using characteristic identities. We discuss how such eigenvalues are …
Combinatorial bases for covariant representations of the Lie superalgebra gl (m| n)
AI Molev - arXiv preprint arXiv:1010.0463, 2010 - arxiv.org
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 …
powers of the natural (m+ n)-dimensional representation. We construct a basis of each …
Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl (m| n)
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 …
(m| n), we use characteristic identities to derive explicit matrix element formulae for all gl (m …
Characteristic identities for Lie (super) algebras
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 …
outline methods that employ these characteristic identities to deduce matrix elements of …
Parabosons, parafermions and representations of ℤ2× ℤ2-graded Lie superalgebras
NI Stoilova, J Van der Jeugt - Journal of Physics: Conference …, 2019 - iopscience.iop.org
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 …
ways to unify them in a larger algebraic structure. One of these corresponds to the …
Super tableaux and a branching rule for the general linear Lie superalgebra
S Clark, YN Peng… - Linear and Multilinear …, 2015 - Taylor & Francis
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 …
Lie superalgebra. Our branching rules depend on the conjugacy class of a Borel …