Classification of Structure Constants for W-algebras from Highest Weights

Details Classification of Structure Constants for W-algebras from Highest Weights Classification of Structure Constants for W-algebras from Highest Weights

1993-07-28

arxiv.org/abs/hep-th/9307170v1

Nucl.Phys. B411 (1994) 307-320

Physics

High Energy Physics

High Energy Physics - Theory

18 pages (A4), LaTeX, DFTT-40/93

Scientific paper

10.1016/0550-3213(94)90061-2

We show that the structure constants of W-algebras can be grouped according to the lowest (bosonic) spin(s) of the algebra. The structure constants in each group are described by a unique formula, depending on a functional parameter h(c) that is characteristic for each algebra. As examples we give the structure constants C_{33}^4 and C_{44}^4 for the algebras of type W(2,3,4,...) (that include the WA_{n-1}-algebras) and the structure constant C_{44}^4 for the algebras of type W(2,4,...), especially for all the algebras WD_n, WB(0,n), WB_n and WC_n. It also includes the bosonic projection of the super-Virasoro algebra and a yet unexplained algebra of type W(2,4,6) found previously.

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