Ext-group in the category of quantum polynomial functors via the quantum Frobenius twist

Abstract

We study the effect of a quantum Frobenius twist on Ext-groups in the category of quantum polynomial functors. We use quantum versions of the de Rham and Koszul complexes, and compute their homologies. We use them to do several Ext-computations, and obtain a formula to compute Ext-groups between two functors obtained via the Frobenius, in characteristic zero or in big enough characteristic. Finally, we make some advancements toward a general formula in arbitrary characteristic.