SL(2,Z)-Invariant Spaces Spanned by Modular Units

Details SL(2,Z)-Invariant Spaces Spanned by Modular Units SL(2,Z)-Invariant Spaces Spanned by Modular Units

1997-04-03

arxiv.org/abs/q-alg/9704004v2

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTeX2e (+amsfonts, amsopn, amsthm, amsmath)

Scientific paper

Characters of rational vertex operator algebras (RVOAs) arising in 2-dimensional conformal field theories often belong (after suitable normalization) to the (multiplicative) semigroup E^+ of modular units whose Fourier expansions are in 1+q Z_{>=0}[[q]], up to a fractional power of q. If even all characters of a RVOA share this property then we have an example of what we call modular sets, i.e. finite subsets of E^+ whose elements (additively) span a vector space which is invariant under the usual action of SL(2,Z). The classification of modular sets and RVOAs seem to be closely related. In this article we give an explicit description of the group of modular units generated by E^+, we prove a certain finiteness result for modular sets contained in a natural semi-subgroup E_* of E^+, and we discuss consequences.

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