14 citations · 44 across the 7 of their papers we have counts for
8 papers
Explicit conserved operators for a class of integrable bosonic networks from the classical Yang-Baxter equation
Phillip S. Isaac, Jon Links, Inna Lukyanenko +1
Let denote the weighted adjacency matrix of a balanced, symmetric, bipartite graph. We define a class of bosonic networks given by Hamiltonians whose hopping terms are determin…
Invariants and reduced Wigner coefficients for quasi-triangular Hopf superalgebras
Mark D. Gould, Phillip S. Isaac, Jason L. Werry
We develop explicit formulae for the eigenvalues of various invariants for highest weight irreducible representations of the quantum supergroup . The techniques emplo…
New R-matrices with non-additive spectral parameters and integrable models of strongly correlated fermions
Yao-Zhong Zhang, Jason L. Werry
We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from…
Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond
Jason L. Werry, Phillip S. Isaac, Mark D. Gould
In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in…
Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)
Jason L. Werry, Mark D. Gould, Phillip S. Isaac
The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible modules. In particular,…
Characteristic identities for Lie (super)algebras
Phillip S. Isaac, Jason L. Werry, Mark D. Gould
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…
Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)
Mark D. Gould, Phillip S. Isaac, Jason L. Werry
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 al…
Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)
Mark D. Gould, Phillip S. Isaac, Jason L. Werry
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 relate…