Abstract: Cyclic quotient singularities are the first interesting examples of normal affine toric varieties that are singular. The torus action gives a description of the variety and torus invariant Weil divisors in terms of combinatorics. Having this information, we derive a combinatorial description of the Ext-modules of two torus invariant Weil divisors and prove a certain symmetry. Finally we show a duality of the Ext-modules with certain Tor-modules.