Induced representations defined in terms of tensor products of $G$ modules and in terms of vector-valued functions on $G$. It would be nice, if more textbook in representation theory stress this more heavily. Both definition have their advantages and disadvantages, I guess, but I personally feel more comfortable with the interpretation in terms of functions.
Induction defined in terms of tensor products of $G$ modules and in terms of vector-valued functions on $G$. It would be nice, if more textbook in representation theory stress this more heavily. Both definition have their advantages and disadvantages, I guess, but I personally feel more comfortable with the interpretation in terms of functions.