The Poincare series of a quasihomogeneous surface singularity

The Poincare series p_A(t) of the coordinate algebra A of a normal surface singularity (X, x) with good C*-action is written in a certain way as a quotient of two polynomials #phi#_A(T)/#psi#_A(t). For a Kleinian singularity, we derive from the McKay correspondence that #phi#_A(t) and #psi#_A(t) are the characteristic polynomials of the Coxter element and the affine Coxeter element respectively. We show that if (X, x) is a hypersurface singularity or a certain ICIS then #phi#_A(t) is in a certain sense dual to the characteristic polynomial of the monodromy operator of the singularity. There are relations to the mirror symmetry of K3 surfaces and to automorphisms of the Leech lattice. (orig.)SIGLEAvailable from TIB Hannover: RN 3109(301) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman