Modular forms and almost linear dependence of graded dimensions
Abstract
Description
For every positive integral level $k$ we study arithmetic properties of certain holomorphic modular forms associated to modular invariant spaces spanned by graded dimensions of $L_{\hat{sl_2}}(k Λ_0)$-modules. We found a necessary and sufficient condition for their vanishing and showed that these modular forms resemble classical Eisenstein series $E_{2k+2}(τ)$. Furthermore, we derived similar results for $\mathcal{M}(p,p')$ Virasoro minimal models, thus generalizing some results of Mortenson, Ono and the author.
Presented at the conference "Lie Algebras, Vertex Operator Algebras and Their Applications" NCSU, May 2005
Presented at the conference "Lie Algebras, Vertex Operator Algebras and Their Applications" NCSU, May 2005