$Z^N$-graded Lie algebras: Fock representations and reducibility conditions

Details $Z^N$-graded Lie algebras: Fock representations and reducibility conditions $Z^N$-graded Lie algebras: Fock representations and reducibility conditions

1992-12-09

arxiv.org/abs/hep-th/9212055v1

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 21 pages

Scientific paper

Manifestly consistent Fock representations of non-central (but ``core-central'') extensions of the $Z^N$-graded algebras of functions and vector fields on the $N$-dimensional torus $T^N$ are constructed by a kind of renormalization procedure. These modules are of lowest-energy type, but the energy is not a linear function of the momentum. Modulo a technical assumption, reducibility conditions are proved for the extension of $vect(T^N)$, analogous to the discrete series of Virasoro representations.

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