14 citations · 39 across the 4 of their papers we have counts for
22 papers
Development of a unified tensor calculus for the exceptional Lie algebras
A. J. Macfarlane, Hendryk Pfeiffer
The uniformity of the decomposition law, for a family F of Lie algebras which includes the exceptional Lie algebras, of the tensor powers ad^n of their adjoint representations ad i…
Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator
A. J. Macfarlane, Hendryk Pfeiffer
The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is well-known now for powers up to the fourth. Th…
Lie algebra and invariant tensor technology for g2
A. J. Macfarlane
Proceeding in analogy with su(n) work on lambda matrices and f- and d-tensors, this paper develops the technology of the Lie algebra g2, its seven dimensional defining representati…
Hidden supersymmetries in supersymmetric quantum mechanics
J. A. de Azcárraga, J. M. Izquierdo, A. J. Macfarlane
We discuss the appearance of additional, hidden supersymmetries for simple 0+1 -invariant supersymmetric models and analyse some geometrical mechanisms that lead to them. It…
Symplectic and orthogonal Lie algebra technology for bosonic and fermionic oscillator models of integrable systems
A. J. Macfarlane, H. Pfeiffer, F. Wagner
To provide tools, especially L-operators, for use in studies of rational Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N) (b_n, d_n) or sp(2n) (c_n) a…
Monopole supersymmetries and the Biedenharn operator
P. A. Horváthy, A. J. Macfarlane, J. -W. van Holten
The hidden supersymmetry of the monopole found by De Jonghe et al. is generalized to a spin $\2$ particle in the combined field of a Dirac monopole plus a potential [cons…