In his thesis, Schraen computes various (higher) Ext groups between locally analytic generalized Steinberg representations for GL3(Qp), which leads to his definition for L invariants for GL3(Qp). We generalize Schraen’s computation to GLn and thus give a new definition for all L invariants for GLn simultaneously, using higher Ext groups and cup products between them. The main ingredient is a new combinatorial trick to compute the spectral sequence involved. If time permits, we may sketch the relation to Drinfeld space (as in Schaen’s thesis), or the relation to Breuil-Ding’s result.