In a recent paper [7], Erdmann has calculated Ext1G between Weyl modules for SL2. In this paper we generalize this result to solve the corresponding problem for quantum GL2 as defined by Dipper and Donkin in [2]. We also show how our result also holds for the Manin quantization. To apply the methods of [7], it is necessary to determine the block structure of quantum GL2, so the first main result of this paper is a description of this, derived from the analysis of the subcomodule structure of the symmetric powers in [10].

After an initial section of generalities, the next section consists of the determination of the block structure. We also need a quantum analogue of two short exact sequences from [11], which we give in the following section. With these results, the argument now follows much as in [7]; we consider the infinitesimal case, and then use the Lyndon–Hochschild–Serre spectral sequence to obtain the desired result. Finally we show how the result also holds for the Manin quantization.

It should be noted that the result here uses the classical case, so is not independent of that in [7]. The only real difference in the arguments used occurs in Lemma 4·8 where the original methods do not generalize, so we use a more direct argument. There is also an unfortunate typographical error in the statement of the main result in [7].