arXiv subjects
Publications and source records attributed to K. Bugajska.
We investigate algebraic structures related to triangle decompositions of a moduli space of complex tori given by the Veech curve T*. We show that these structures produce the binary error correcting Golay code G_{24}
We show that for supersingular prime p the image of a unique meromorphic function G_p on X_0(p) (of degree two, with polar divisor {[0]_0,[\infty]_0}) under a certain Hecke operator is equal to j(τ) (up to some additional constant). This generates quantities of relations between the coefficients of j(t) and leads to some group of hidden symmetries whose order must be divided by p.
We examine the moduli space E=T* of complex tori T(t)=C/L(t) where L(t)=cost.n(t)Lt. We find that the Dedekind eta function furnishes a bridge between the euclidean and hyperbolic structures on T*=C-L/L as well as between the doubly periodic Weierstrass function p on T* and the theta function for the lattice E(8). The former one allows us to rewrite the Lame equation for the Bers embedding of T(1,1) in a new form. We show that L has natural decomposition into 8 sublattices (each equivalent to L) together with appropriate half-points and that this leads to some local functions and to a relation with E(8)
We show that for any fixed point P on a Riemann surface S the distinct realizations of cocycles in H^1(S,O) correspond to the natural appearence of the standard Heisenberg vertex operator algebra II(P) and to the commutative Heisenberg vertex operator algebra II*(P) respectively