Abstract: A novel algebraic approach recently proposed is presented in this paper for investigating the \tau lepton decay process. In this approach, we use the basic weak interaction and angular momentum algebra and finally obtain analytical decay amplitudes, finding that this formalism can relate the different decay processes and also lead to a different interpretation of the important role played by G-parity in these decays. Then we apply this formalism to explore some meaningful and interesting applications on \tau lepton decays, including the polarization amplitudes and tests on the nature of scalar resonances or axial-vector resonances. The results show that one magnitude is very sensitive to the \alpha parameter and useful to test different models Beyond the Standard Model. And very importantly, we firstly open up a new direction in the \tau decays to test the nature of resonances which were obtained as dynamically generated from the pseudoscalar-pseudoscalar or vector-pseudoscalar interactions. In these \tau decays we make predictions for invariant mass distribution and the final branching ratios, the results show that these ratios are within measurable ranges on related experiments in the possible future large research facility of the Super Tau-Charm Facility of China.