New answers tagged

1

Since $f(x)$ must be either constant or balanced, there are only 4 possibilities for what $f(x)$ could be. For each of these four cases, you can explicitly write $U_f$ as a matrix, which you can easily check for unitarity.


2

No there are none (apart from the trivial rep.). This follows not because of the metric but because the transformations on Euclidean space still form a non-compact group, like Poincaré. The best you can do apparently is to have indecomposable representations, and that’s a mess because that representation theory is “wild”. The case of $E(2)$ is somewhat ...


Top 50 recent answers are included