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We show that the conformal characters of various rational models of W-algebras can be already uniquely determined if one merely knows the central charge and the conformal dimensions. As a side result we develop several tools for studying representations of SL(2,Z) on spaces of modular functions. These methods, applied here only to certain rational conformal… (More)
We describe the construction of vector valued modular forms transforming under a given congruence representation of the modular group SL(2, Z) in terms of theta series. We apply this general setup to obtain closed and easily computable formulas for conformal characters of rational models of W-algebras.
Jacobi forms can be considered as vector valued modular forms, and Jacobi forms of critical weight correspond to vector valued modular forms of weight 1 2 . Since the only modular forms of weight 1 2 on congruence subgroups of SL(2,Z) are theta series the theory of Jacobi forms of critical weight is intimately related to the theory of Weil representations… (More)
The Rankin convolution type Dirichlet series DF,G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series DF,G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of… (More)
We describe several infinite series of rational conformal field theories whose conformal characters are modular units, i.e. which are modular functions having no zeros or poles in the upper complex half plane, and which thus possess simple product expansions. We conjecture that certain infinite series of rational models of Casimir W-algebras always have… (More)
We state ready to compute dimension formulas for the spaces of Jacobi cusp forms of integral weight k and integral scalar index m on subgroups of SL(2,Z).
We discuss the notion of Jacobi forms of degree one with matrix index, we state dimension formulas, give explicit examples, and indicate how closely their theory is connected to the theory of invariants of Weil representations associated to finite quadratic modules. 1 Jacobi forms of degree one Jacobi forms of degree one with matrix index F gained recent… (More)
We describe the construction of vector valued modular forms transforming under a given congruence representation of the modular group SL(2,Z) in terms of theta series. We apply this general setup to obtain closed and easily computable formulas for conformal characters of rational models of W-algebras. 2 Université Bordeaux I, UFR de Mathématiques et… (More)
Preface These are the notes of a course on Lie algebras which I gave at the university of Bordeaux in spring 1997. The course was a so-called \Cours PostDEA", and as such had to be held within 12 hours. Even more challenging, no previous knowledge about Lie algebras should be assumed. Nevertheless, I had the goal to reach as peak of the course the character… (More)
It is proved that the theta series of an even lattice whose level is a power of a prime l is congruent modulo l to an elliptic modular form of level 1. The proof uses arithmetic and algebraic properties of lattices rather than methods from the theory of modular forms. The methods presented here may therefore be especially pleasing to those working in the… (More)