Generalized spatial modulation (GSM) has come up as a spectrally efficient transmission scheme for high data rate applications as the information bits are transmitted in multiple dimensions by the selective activation of the transmit antennas, unlike the conventional schemes employing phase and amplitude-based modulations alone. Differential schemes for modulation are essential for receivers having strict energy and processing power constraints since these schemes do not require frequent channel estimation at the receiver. Differential schemes for GSM improve the spectral efficiency in comparison with conventional differential schemes for spatial modulation (SM) with only a nominal increase in the number of transmit antennas. However ML-based detectors require intensive processing at the receiver. In this paper, a simplified detector based on geometric approximation of the received signal is proposed for the differential schemes of GSM. Firstly, the two-stage detector selects a reduced set of candidates for the transmit antenna combinations based on the correlation with the received signal. A joint detection is performed with the l2 -norm minimization approach, on the reduced sets of antenna combinations, along with the modulated symbols lying in the vicinity of the dominant eigenvector of the received signal, to detect the transmitted symbol. The proposed detector has a significant reduction in complexity along with a comparable error performance with respect to the optimal detector.