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The 2-parameter Green functions occur as a crucial ingredient in thecharacter formula for Lusztig induction in finite reductive groups. Still, verylittle is known about these functions, in particular in the case of groupsarsing from algebraic groups with disconnected centre. We collect some basicproperties and then apply these, together with some explicit computations, todetermine all 2-parameter Green functions for 8-dimensional spin groups in oddcharacteristic, whose centre is disconnected of order~4.

The 2-parameter Green functions for 8-dimensional spin groups