Simple Groups and Strong Interaction Symmetries

LIE ALGEBRA AND INVARIANT TENSOR TECHNOLOGY FOR g2

“…This search studied g 2 and its representations using roots and weights within the Cartan-Weyl description of Lie algebras. The papers [8] [20] are still excellent accounts of this work. Many physicist at this time relied on [21] for their understanding of Lie algebra theory.…”

“…This is explained in [8] and in many other places; the discussion in [25] contains relevant detail but does not stress it in the g 2 context.…”

“…We begin by giving references that have been found useful for general background information on Lie algebras [1][2][3][4][5], and for detailed information [6][7][8][9][10] on the exceptional Lie algabra g 2 . For some indication of the programme we are aiming to follow for g 2 , we cite [11] a study of some integrable systems with the invariance algebra c n = sp(2n, R).…”

“…See also [28] (as well as [8]) for information about g 2 characters and branching rules. Finally we cite some interesting work on non-compact realisations of G 2 [35][36][37][38].…”

Intrinsic formulae for the Casimir operators of semidirect products of the exceptional Lie algebraG2and a Heisenberg Lie algebra

“…The same procedure can be applied to the higher rank exceptional algebras, but the low dimension of G 2 and its particular properties make it the adecuate frame for computations. The interest of a synthetic procedure for these algebras is out of discussion, for the various physical applications of exceptional algebras, as the labelling of internal states, since they entered elementary particle physics in the beginning sixties ( [12,13] and references therein), and which constitute nowadays an important tool in high energy physics.…”